32581 + Interview Questions in Mathematics Page 144 InterviewSolution

7151.	39. What is the formula of vertex of a quadratic eqn while drawing it's graph?
Answer» 39. What is the formula of vertex of a quadratic eqn while drawing it's graph?

Discussion

7152.	How to find zeroes of a biquadratic polynomial.
Answer» How to find zeroes of a biquadratic polynomial.

Discussion

7153.	α,β are zeros of polynomial 2x^2+6x-3 find the value of:-- α^3β+β^3α,[ α_β]^2,α+1/α+β1/β,α^2/β+β^2β,1/α+1/β
Answer» α,β are zeros of polynomial 2x^2+6x-3 find the value of:-- α^3β+β^3α,[ α_β]^2,α+1/α+β1/β,α^2/β+β^2β,1/α+1/β

Discussion

7154.	There are 25 red balls, 42 blue balls and 33 yellow balls in a bag. Kiran mixes the balls thoroughly inside the bag and then picks a ball at random from the bag. What is the probability that Kiran picks a blue ball?
Answer» There are 25 red balls, 42 blue balls and 33 yellow balls in a bag. Kiran mixes the balls thoroughly inside the bag and then picks a ball at random from the bag. What is the probability that Kiran picks a blue ball?

Discussion

7155.	If the radii of circular ends of frustum of a cone are 20 cm and 12 cm and its height is 6 cm, then the slant height of frustum (in cm) is:
Answer» If the radii of circular ends of frustum of a cone are 20 cm and 12 cm and its height is 6 cm, then the slant height of frustum (in cm) is:

Discussion

7156.	Find the values of other trigonometric ratios, given that: cosec theta= √1+√m^4÷√n^4
Answer» Find the values of other trigonometric ratios, given that: cosec theta= √1+√m^4÷√n^4

Discussion

7157.	A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, find : (i) its radius, (ii) its slant height. [3 MARKS]
Answer» A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, find : (i) its radius, (ii) its slant height. [3 MARKS]

Discussion

7158.	A sum of amount X earns simple interest of Rs. 1250 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
Answer» A sum of amount $X$ earns simple interest of Rs. 1250 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

Discussion

7159.	A milk carrying container has the shape of a cylinder mounted on a frustum. The radius of the cylinder is 14 cm and height is 20 cm. The other diameter of the frustum is 7 cm and its height is 5 cm. What is the curved surface area of the container?
Answer» A milk carrying container has the shape of a cylinder mounted on a frustum. The radius of the cylinder is 14 cm and height is 20 cm. The other diameter of the frustum is 7 cm and its height is 5 cm. What is the curved surface area of the container?

Discussion

7160.	The roster form of A = {Prime numbers between 10 and 20} is ___.
Answer» The roster form of A = {Prime numbers between 10 and 20} is ___.

7160.

The roster form of A = {Prime numbers between 10 and 20} is ___.

Answer»

The roster form of A = {Prime numbers between 10 and 20} is ___.

Discussion

7161.	the radii of two spheres made of same metal are r and 2r. These are heated to the same temperature and placed in the same surrounding. The ratio of rates of decrease of their temperature will be (1) 1:1 (2) 4:1 (3) 1:4 (4) 2:1
Answer» the radii of two spheres made of same metal are r and 2r. These are heated to the same temperature and placed in the same surrounding. The ratio of rates of decrease of their temperature will be (1) 1:1 (2) 4:1 (3) 1:4 (4) 2:1

Discussion

7162.	In ∆ABC, ∠A is obtuse, PB ⊥ AC and QC ⊥ AB. Prove that:(i) AB ✕ AQ = AC ✕ AP(ii) BC2 = (AC ✕ CP + AB ✕ BQ)
Answer» In ∆ABC, ∠A is obtuse, PB ⊥ AC and QC ⊥ AB. Prove that: (i) AB ✕ AQ = AC ✕ AP (ii) BC² = (AC ✕ CP + AB ✕ BQ)

Discussion

7163.	ABC is a ∆ with AB = 10 cm, BC = 8 cm & AC = 6 cm. 3 circles are drawn touching each other with the vertices at their centers. Find the radii of the 3 circles.
Answer» ABC is a ∆ with AB = 10 cm, BC = 8 cm & AC = 6 cm. 3 circles are drawn touching each other with the vertices at their centers. Find the radii of the 3 circles.

7163.

ABC is a ∆ with AB = 10 cm, BC = 8 cm & AC = 6 cm. 3 circles are drawn touching each other with the vertices at their centers. Find the radii of the 3 circles.

Answer»

ABC is a ∆ with AB = 10 cm, BC = 8 cm & AC = 6 cm. 3 circles are drawn touching each other with the vertices at their centers. Find the radii of the 3 circles.

Discussion

7164.	Solve for x : 12x−3+1x−5=119,x≠32,5
Answer» Solve for x : $\frac{1}{2 x - 3} + \frac{1}{x - 5} = 1 \frac{1}{9}, x \neq \frac{3}{2}, 5$

Discussion

7165.	Let a point P moves such that the sum of squares of it's distance from the planes P1:x−y−z=0 and P2:y−z=0 is always equal to the square of it's distance from the plane P3:x−2y+z=0. Then the locus of point P is:
Answer» Let a point $P$ moves such that the sum of squares of it's distance from the planes $P_{1} : x - y - z = 0$ and $P_{2} : y - z = 0$ is always equal to the square of it's distance from the plane $P_{3} : x - 2 y + z = 0.$ Then the locus of point $P$ is:

Discussion

7166.	Ten men take 4 days to complete the task of tarring a road. How many days would 8 men take?
Answer» Ten men take 4 days to complete the task of tarring a road. How many days would 8 men take?

Discussion

7167.	The expression x4+8x2+16 can be factorized as:
Answer» The expression $x^{4} + 8 x^{2} + 16$ can be factorized as:

Discussion

7168.	Identify the major sector and minor segment in the given figure:
Answer» Identify the major sector and minor segment in the given figure:

Discussion

7169.	If the radius of a sphere is 12 cm, then find its total surface area . (Take π=3.14)
Answer» If the radius of a sphere is 12 cm, then find its total surface area . (Take $π = 3.14)$

Discussion

7170.	Question 7A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
Answer» Question 7 A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Discussion

7171.	In Q. No. 9, what is the value of a2bc+b2ca+c2ab?
Answer» In Q. No. 9, what is the value of $\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}$ ?

Discussion

7172.	D is a point on the side BC of a ΔABC such that ∠ADC=∠BAC. Show that CA2=CB.CD.
Answer» D is a point on the side BC of a $Δ A B C$ such that $∠ A D C = ∠ B A C$ . Show that $C A^{2} = C B . C D$ .

7172.

D is a point on the side BC of a ΔABC such that ∠ADC=∠BAC. Show that CA2=CB.CD.

Answer»

D is a point on the side BC of a $Δ A B C$ such that $∠ A D C = ∠ B A C$ . Show that $C A^{2} = C B . C D$ .

Discussion

7173.

Write the median class for the following frequency distribution: Class-interval: 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency: 5 8 7 12 28 20 10 10

Answer» Write the median class for the following frequency distribution:

Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	5	8	7	12	28	20	10	10

Discussion

7174.	In the given G.P find the product of the fifth term from the begining and from the end. 116,14,1,4,16.........16,384.
Answer» In the given G.P find the product of the fifth term from the begining and from the end. $\frac{1}{16}, \frac{1}{4}, 1, 4, 16.........16, 384.$

7174.

In the given G.P find the product of the fifth term from the begining and from the end. 116,14,1,4,16.........16,384.

Answer»

In the given G.P find the product of the fifth term from the begining and from the end.

$\frac{1}{16}, \frac{1}{4}, 1, 4, 16.........16, 384.$

Discussion

7175.	Show that root 3 +root 5 is an irrational number
Answer» Show that root 3 +root 5 is an irrational number

Discussion

7176.	Choose the correct answer in each of the following questions:The sum of first n terms of an AP is (4n2 + 2n). The nth term of the AP is (a) (6n − 2) (b) (7n − 3) (c) (8n − 2) (d) (8n + 2) [CBSE 2014]
Answer» Choose the correct answer in each of the following questions: The sum of first n terms of an AP is (4n² + 2n). The nth term of the AP is (a) (6n − 2) (b) (7n − 3) (c) (8n − 2) (d) (8n + 2) [CBSE 2014]

Discussion

7177.	If A=diag(4,5,9) and B=diag(−1,−2,−4), then 2A+4B is:
Answer» If $A = diag (4, 5, 9)$ and $B = diag (- 1, - 2, - 4)$ , then $2 A + 4 B$ is:

Discussion

7178.	29.volumes of 2 spheres are in the ratio 24:27.find the ratio of their surface areas.
Answer» 29.volumes of 2 spheres are in the ratio 24:27.find the ratio of their surface areas.

Discussion

7179.	If α and β are zeroes of the quadratic polynomial x^2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.
Answer» If α and β are zeroes of the quadratic polynomial x^2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.

Discussion

7180.	In the given circle with centre O, ∠ABC = 100o, ∠ACD = 40o & CT is a tangent to the circle at C. Find ∠DCT.
Answer» In the given circle with centre O, ∠ABC = 100^o, ∠ACD = 40^o & CT is a tangent to the circle at C. Find ∠DCT.

7180.

In the given circle with centre O, ∠ABC = 100o, ∠ACD = 40o & CT is a tangent to the circle at C. Find ∠DCT.

Answer»

In the given circle with centre O, ∠ABC = 100^o, ∠ACD = 40^o & CT is a tangent to the circle at C. Find ∠DCT.

Discussion

7181.	14. The sum of ages of Friends is 20 years four years ago the product of their ages was 48 show that these statements can not be true
Answer» 14. The sum of ages of Friends is 20 years four years ago the product of their ages was 48 show that these statements can not be true

Discussion

7182.	Mark the correct alternative in each of the following:The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is(a) 225 cm2(b) 240 cm2(c) 2252 cm2(d) 450 cm2
Answer» Mark the correct alternative in each of the following: The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is (a) 225 cm² (b) 240 cm² (c) $225 \sqrt{2}$ cm² (d) 450 cm²

Discussion

7183.	Find the area of the sector of a circle having radius 6 cm and of angle 30°. [Take π = 3.14]
Answer» Find the area of the sector of a circle having radius 6 cm and of angle 30°. [Take π = 3.14]

Discussion

7184.	How to find weather the number is rational number
Answer» How to find weather the number is rational number

Discussion

7185.	The number of integral value(s) of a such that the extremum points of f(x)=3x3+7x2+9(a2−4)x+2 are of opposite sign
Answer» The number of integral value(s) of $a$ such that the extremum points of $f (x) = 3 x^{3} + 7 x^{2} + 9 (a^{2} - 4) x + 2$ are of opposite sign

Discussion

7186.	In the given figure, if AOB is a diameter and ∠ADC = 120° , then ∠CAB = ___________
Answer» In the given figure, if AOB is a diameter and ∠ADC = 120° , then ∠CAB = ___________

Discussion

7187.	In two triangles ABC and DEF, ∠A = ∠D and the sum of the angles A and B is equal to the sum of the angles D and E. If BC = 6 cm and EF = 8 cm, then ar(∆ABC) : ar(∆DEF) = ___________.
Answer» In two triangles ABC and DEF, ∠A = ∠D and the sum of the angles A and B is equal to the sum of the angles D and E. If BC = 6 cm and EF = 8 cm, then ar(∆ABC) : ar(∆DEF) = ___________.

Discussion

7188.	Find the value of the polynomial 5x−4x2+3 at(i) x = 0(ii) x = - 1(iii) x = 2
Answer» Find the value of the polynomial $5 x - 4 x^{2} + 3$ at (i) x = 0 (ii) x = - 1 (iii) x = 2

Discussion

7189.	The HCF of the polynomials x^3-3x^2+7x-5 and x^2+5-2x is
Answer» The HCF of the polynomials x^3-3x^2+7x-5 and x^2+5-2x is

Discussion

7190.	(a+b) = 12 ab= 2 find the vakye of (a cube +b cub
Answer» (a+b) = 12 ab= 2 find the vakye of (a cube +b cub

Discussion

7191.	If figure common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
Answer» If figure common tangents AB and CD to two circles intersect at E. Prove that AB = CD.

Discussion

7192.	In ΔABC AM is a median. Calculate: i) The equation of AM ii) The eqation of AN
Answer» In ΔABC AM is a median. Calculate: i) The equation of AM ii) The eqation of AN

7192.

In ΔABC AM is a median. Calculate: i) The equation of AM ii) The eqation of AN

Answer»

In ΔABC AM is a median. Calculate:

i) The equation of AM

ii) The eqation of AN

Discussion

7193.	Question 3 A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years. Age (in years)Number of policy holdersBelow 202Below 256Below 3024Below 3545Below 4078Below 4589Below 5092Below 5598Below 60100
Answer» Question 3 A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years. $\begin{matrix} A g e (i n y e a r s) & N u m b e r o f p o l i c y h o l d e r s B e l o w 20 & 2 B e l o w 25 & 6 B e l o w 30 & 24 B e l o w 35 & 45 B e l o w 40 & 78 B e l o w 45 & 89 B e l o w 50 & 92 B e l o w 55 & 98 B e l o w 60 & 100 \end{matrix}$

7193.

Question 3 A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years. Age (in years)Number of policy holdersBelow 202Below 256Below 3024Below 3545Below 4078Below 4589Below 5092Below 5598Below 60100

Answer»

Question 3
A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.

$\begin{matrix} A g e (i n y e a r s) & N u m b e r o f p o l i c y h o l d e r s B e l o w 20 & 2 B e l o w 25 & 6 B e l o w 30 & 24 B e l o w 35 & 45 B e l o w 40 & 78 B e l o w 45 & 89 B e l o w 50 & 92 B e l o w 55 & 98 B e l o w 60 & 100 \end{matrix}$

Discussion

7194.	If cotθ=13, then write the value of 1-cos2θ2-sin2θ.
Answer» $If \cot θ = \frac{1}{\sqrt{3}}, then write the value of \frac{(1 - \cos^{2} θ)}{(2 - \sin^{2} θ)} .$

Discussion

7195.	Find the ratio of the areas of two similar triangles ABC and PQR shown in the figure where AM and PN are the medians of the △ABC and △PQR respectively.
Answer» Find the ratio of the areas of two similar triangles ABC and PQR shown in the figure where AM and PN are the medians of the $△$ ABC and $△$ PQR respectively.

7195.

Find the ratio of the areas of two similar triangles ABC and PQR shown in the figure where AM and PN are the medians of the △ABC and △PQR respectively.

Answer»

Find the ratio of the areas of two similar triangles ABC and PQR shown in the figure where AM and PN are the medians of the $△$ ABC and $△$ PQR respectively.

Discussion

7196.	Co-ordinates of some pairs of points are given below. Hence find the distance between each pair. (i) 3, 6 (ii) − 9, - 1 (iii)- 4, 5 (iv) x,- 2(v) x + 3, x- 3 (vi) -25,-47 (vii) 80, - 85
Answer» Co-ordinates of some pairs of points are given below. Hence find the distance between each pair. (i) 3, 6 (ii) − 9, $-$ 1 (iii) $-$ 4, 5 (iv) x, $-$ 2 (v) x + 3, x $-$ 3 (vi) $-$ 25, $-$ 47 (vii) 80, $-$ 85

Discussion

7197.	In the figure AB = BC and AD is perpendicular to CD. Prove that : AC2 = 2BC. DC.
Answer» In the figure AB = BC and AD is perpendicular to CD. Prove that : AC² = 2BC. DC.

Discussion

7198.	A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a king.
Answer» A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a king.

Discussion

7199.	The midpoints of the sides BC, CA and AB of a △ABC are D(3, 4), E(8, 9) and F(6, 7) respectively. Find the coordinates of hte vertices of the triangle.
Answer» The midpoints of the sides BC, CA and AB of a $△ A B C$ are D(3, 4), E(8, 9) and F(6, 7) respectively. Find the coordinates of hte vertices of the triangle.

Discussion

7200.	A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed. ___
Answer» A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed. ___

Discussion

Explore topic-wise InterviewSolutions in .

39. What is the formula of vertex of a quadratic eqn while drawing it's graph?

How to find zeroes of a biquadratic polynomial.

α,β are zeros of polynomial 2x^2+6x-3 find the value of:-- α^3β+β^3α,[ α_β]^2,α+1/α+β1/β,α^2/β+β^2β,1/α+1/β

There are 25 red balls, 42 blue balls and 33 yellow balls in a bag. Kiran mixes the balls thoroughly inside the bag and then picks a ball at random from the bag. What is the probability that Kiran picks a blue ball?

If the radii of circular ends of frustum of a cone are 20 cm and 12 cm and its height is 6 cm, then the slant height of frustum (in cm) is:

Find the values of other trigonometric ratios, given that: cosec theta= √1+√m^4÷√n^4

A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, find : (i) its radius, (ii) its slant height. [3 MARKS]

A sum of amount X earns simple interest of Rs. 1250 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

A milk carrying container has the shape of a cylinder mounted on a frustum. The radius of the cylinder is 14 cm and height is 20 cm. The other diameter of the frustum is 7 cm and its height is 5 cm. What is the curved surface area of the container?

The roster form of A = {Prime numbers between 10 and 20} is ___.

the radii of two spheres made of same metal are r and 2r. These are heated to the same temperature and placed in the same surrounding. The ratio of rates of decrease of their temperature will be (1) 1:1 (2) 4:1 (3) 1:4 (4) 2:1

In ∆ABC, ∠A is obtuse, PB ⊥ AC and QC ⊥ AB. Prove that:(i) AB ✕ AQ = AC ✕ AP(ii) BC2 = (AC ✕ CP + AB ✕ BQ)

ABC is a ∆ with AB = 10 cm, BC = 8 cm &amp; AC = 6 cm. 3 circles are drawn touching each other with the vertices at their centers. Find the radii of the 3 circles.

Solve for x : 12x−3+1x−5=119,x≠32,5

Let a point P moves such that the sum of squares of it's distance from the planes P1:x−y−z=0 and P2:y−z=0 is always equal to the square of it's distance from the plane P3:x−2y+z=0. Then the locus of point P is:

Ten men take 4 days to complete the task of tarring a road. How many days would 8 men take?

The expression x4+8x2+16 can be factorized as:

Identify the major sector and minor segment in the given figure:

If the radius of a sphere is 12 cm, then find its total surface area . (Take π=3.14)

Question 7A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

In Q. No. 9, what is the value of a2bc+b2ca+c2ab?

D is a point on the side BC of a ΔABC such that ∠ADC=∠BAC. Show that CA2=CB.CD.

Write the median class for the following frequency distribution: Class-interval: 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency: 5 8 7 12 28 20 10 10

In the given G.P find the product of the fifth term from the begining and from the end. 116,14,1,4,16.........16,384.

Show that root 3 +root 5 is an irrational number

Choose the correct answer in each of the following questions:The sum of first n terms of an AP is (4n2 + 2n). The nth term of the AP is (a) (6n − 2) (b) (7n − 3) (c) (8n − 2) (d) (8n + 2) [CBSE 2014]

If A=diag(4,5,9) and B=diag(−1,−2,−4), then 2A+4B is:

29.volumes of 2 spheres are in the ratio 24:27.find the ratio of their surface areas.

If α and β are zeroes of the quadratic polynomial x^2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.

In the given circle with centre O, ∠ABC = 100o, ∠ACD = 40o &amp; CT is a tangent to the circle at C. Find ∠DCT.

14. The sum of ages of Friends is 20 years four years ago the product of their ages was 48 show that these statements can not be true

Mark the correct alternative in each of the following:The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is(a) 225 cm2(b) 240 cm2(c) 2252 cm2(d) 450 cm2

Find the area of the sector of a circle having radius 6 cm and of angle 30°. [Take π = 3.14]

How to find weather the number is rational number

The number of integral value(s) of a such that the extremum points of f(x)=3x3+7x2+9(a2−4)x+2 are of opposite sign

In the given figure, if AOB is a diameter and ∠ADC = 120° , then ∠CAB = ___________

In two triangles ABC and DEF, ∠A = ∠D and the sum of the angles A and B is equal to the sum of the angles D and E. If BC = 6 cm and EF = 8 cm, then ar(∆ABC) : ar(∆DEF) = ___________.

Find the value of the polynomial 5x−4x2+3 at(i) x = 0(ii) x = - 1(iii) x = 2

The HCF of the polynomials x^3-3x^2+7x-5 and x^2+5-2x is

(a+b) = 12 ab= 2 find the vakye of (a cube +b cub

If figure common tangents AB and CD to two circles intersect at E. Prove that AB = CD.

In ΔABC AM is a median. Calculate: i) The equation of AM ii) The eqation of AN

If cotθ=13, then write the value of 1-cos2θ2-sin2θ.

Find the ratio of the areas of two similar triangles ABC and PQR shown in the figure where AM and PN are the medians of the △ABC and △PQR respectively.

Co-ordinates of some pairs of points are given below. Hence find the distance between each pair. (i) 3, 6 (ii) − 9, - 1 (iii)- 4, 5 (iv) x,- 2(v) x + 3, x- 3 (vi) -25,-47 (vii) 80, - 85

In the figure AB = BC and AD is perpendicular to CD. Prove that : AC2 = 2BC. DC.

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a king.

The midpoints of the sides BC, CA and AB of a △ABC are D(3, 4), E(8, 9) and F(6, 7) respectively. Find the coordinates of hte vertices of the triangle.

A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed. ___

ABC is a ∆ with AB = 10 cm, BC = 8 cm & AC = 6 cm. 3 circles are drawn touching each other with the vertices at their centers. Find the radii of the 3 circles.

In the given circle with centre O, ∠ABC = 100o, ∠ACD = 40o & CT is a tangent to the circle at C. Find ∠DCT.