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1.

Find the radius of a circle if 2 m is the length of the tangent, 6 m is the distance between the center of the circle the external point.(a) 7 m(b) 5 m(c) √32 m(d) √38 mThis question was posed to me in my homework.Asked question is from Number of Tangents from a Point on the Circle topic in division Circles of Mathematics – Class 10

Answer»

The correct OPTION is (c) √32 m

For EXPLANATION I would say: Length of the tangent = \(\SQRT {d^2 – R^2}\)

2 = \(\sqrt {6^2 – r^2}\)

r^2 = 6^2 – 2^2

r = \(\sqrt {6^2 – 2^2}\)

r = \(\sqrt {36 – 4}\)

r = √32 m
Discussion
2.

Identify the parts of a circle.(a) Sides(b) Chord(c) Corners(d) FacesThe question was posed to me in an international level competition.Enquiry is from Tangent to a Circle topic in chapter Circles of Mathematics – Class 10

Answer»

Correct choice is (B) Chord

The EXPLANATION: Chord is one of the parts of a CIRCLE. A line segment that joins any two points on a circle is called a chord. The other parts of a circle are arc, segment, SECANT, radius, diameter, ETC.
Discussion
3.

The area of the sector is _____(a) \(\frac {x^{\circ }}{360^{\circ }}\) × πr^2(b) \(\frac {x^{\circ }}{360^{\circ }}\) – πr^2(c) \(\frac {x^{\circ }}{360^{\circ }}\) + πr^3(d) \(\frac {x^{\circ }}{360^{\circ }}\) × πr^3This question was posed to me in an internship interview.The above asked question is from Number of Tangents from a Point on the Circle topic in portion Circles of Mathematics – Class 10

Answer» RIGHT answer is (a) \(\frac {x^{\circ }}{360^{\circ }}\) × πr^2

Explanation: The AREA of the SECTOR is \(\frac {x^{\circ }}{360^{\circ }}\) × πr^2

Where x° is the DEGREE measure of the angle at the center and r is the radius of the circle.
Discussion
4.

The radius is always _____ to the tangent.(a) equal(b) perpendicular(c) twice(d) parallelI got this question in exam.I'm obligated to ask this question of Tangent to a Circle topic in section Circles of Mathematics – Class 10

Answer»

Right choice is (b) perpendicular

Easiest explanation: Radius is measured from the CENTER of the CIRCLE to any point on the circle and it is always perpendicular to the tangent drawn at their COMMON point of contact.
Discussion
5.

Find the length of the tangent if d = 5 cm and r = 4 cm.(a) 3 cm(b) 4 cm(c) 5 cm(d) 9 cmThe question was asked in a national level competition.This intriguing question comes from Tangent to a Circle in division Circles of Mathematics – Class 10

Answer» RIGHT option is (a) 3 cm

For EXPLANATION I WOULD say: The length of the tangent = \(\sqrt {d^2-r^2}\)

= \(\sqrt {5^2-4^2}\)

= √9

= 3
Discussion
6.

A tangent touches a circle at a single point.(a) False(b) TrueI got this question in semester exam.This interesting question is from Number of Tangents from a Point on the Circle in chapter Circles of Mathematics – Class 10

Answer»

Correct option is (b) True

Best explanation: A line that touches/intersects a CIRCLE at exactly one POINT of a circle is called a tangent and an infinite number of tangents are drawn to a circle WHEREAS SECANT is a line that intersects two distinct points on a circle.
Discussion
7.

What happens to the length of the chord when the chord comes closer to the center?(a) Decreases(b) Becomes an arc(c) Increases(d) Becomes a segmentI got this question in an online quiz.My question is from Number of Tangents from a Point on the Circle in chapter Circles of Mathematics – Class 10

Answer»

The correct CHOICE is (C) Increases

Easy explanation: The LENGTH of the CHORD of a circle increases when it comes closer and closer to the center of the circle. Hence, the longest chord becomes the diameter.
Discussion
8.

Find the area of the sector if the radius is 6 cm and with an angle of 60°.(a) 18.35 cm(b) 18.85 cm(c) 18.00 cm(d) 18.05 cmThe question was posed to me in a national level competition.Question is from Number of Tangents from a Point on the Circle topic in section Circles of Mathematics – Class 10

Answer» CORRECT choice is (b) 18.85 cm

To EXPLAIN: The area of the SECTOR = \(\FRAC {x^{\circ }}{360^{\circ }}\) × πr^2

= \(\frac {60^{\circ }}{360^{\circ }}\) x \(\frac {22}{7}\) × 6^2

= 18.85 cm
Discussion
9.

Length of the tangent is _____(a) \(\sqrt {d^2+c^2}\)(b) \(\sqrt {r^2-d^2}\)(c) \(\sqrt {d^2-c^2}\)(d) \(\sqrt {d^2-r^2}\)The question was asked by my college professor while I was bunking the class.My query is from Tangent to a Circle in portion Circles of Mathematics – Class 10

Answer» CORRECT answer is (d) \(\sqrt {d^2-r^2}\)

Explanation: LENGTH of the tangent (l) = \(\sqrt {d^2-r^2}\)

Where, l = Length of the tangent.

d = DISTANCE between center of the circle and the external point of the circle.

r = RADIUS of the circle.
Discussion
10.

Number of tangents passing through a circle is _____(a) 2(b) 3(c) 1(d) 0The question was asked in a national level competition.My doubt is from Number of Tangents from a Point on the Circle topic in portion Circles of Mathematics – Class 10

Answer»

Correct ANSWER is (d) 0

The BEST explanation: A line that touches/intersects a circle at EXACTLY one POINT of a circle is called a TANGENT and a tangent to a circle doesn’t pass through the circle.
Discussion
11.

Find the area of the circle if 8 cm is the length of the tangent, 11 cm is the distance between the center of the circle the external point.(a) 100 cm(b) 110 cm(c) 197.14 cm(d) 179.14 cmThe question was posed to me in class test.My doubt stems from Tangent to a Circle in chapter Circles of Mathematics – Class 10

Answer»

Correct choice is (d) 179.14 cm

Explanation: Length of the tangent = \(\sqrt {d^2-R^2}\)

8 = \(\sqrt {11^2-r^2}\)

r^2 =11^2 – 8^2

r = \(\sqrt {11^2-8^2}\)

r = √57

Area of the CIRCLE = πr^2

= \(\FRAC {22}{7}\)(√57)^2

= 179.14
Discussion
12.

Find the radius of a circle if 8 m is the length of the tangent, 11 m is the distance between the center of the circle the external point.(a) 7 m(b) 5 m(c) √57 m(d) √58 mI have been asked this question in class test.Asked question is from Tangent to a Circle in portion Circles of Mathematics – Class 10

Answer»

The CORRECT option is (C) √57 m

Explanation: Length of the tangent = \(\SQRT {d^2-R^2}\)

8 = \(\sqrt {11^2-r^2}\)

r^2 =11^2 – 8^2

r = \(\sqrt {11^2-8^2}\)

r = \(\sqrt {121-64}\)

r = √57
Discussion
13.

What is the name of the point which is common to circle and the tangent?(a) Intersection point(b) Tangential point(c) Point of contact(d) Point of touchThe question was posed to me in a job interview.My query is from Tangent to a Circle topic in section Circles of Mathematics – Class 10

Answer»

The correct answer is (c) Point of contact

To elaborate: A line that touches/intersects a circle at EXACTLY one point of a circle is called a TANGENT and the point which is COMMON for both circle and tangent is called the point of contact.
Discussion
14.

The angle in a semi-circle is _____(a) 90°(b) 180°(c) 0°(d) 360°This question was addressed to me during an interview.My question is taken from Tangent to a Circle topic in portion Circles of Mathematics – Class 10

Answer» CORRECT ANSWER is (b) 180°

The explanation: The ANGLE in a semi-circle is 180° whereas the angle in a circle is a COMPLETE angle that is 360° and an angle is said to be 0° when the circle is in the form of a point.
Discussion
15.

Choose the correct statement.(a) The center of the circle belongs to the circle(b) The angle in a semi-circle is a complete angle(c) A circle can have only two parallel tangents(d) Radius equals to twice of the diameterI had been asked this question in a job interview.This question is from Tangent to a Circle topic in division Circles of Mathematics – Class 10

Answer»

Right OPTION is (C) A CIRCLE can have only two parallel tangents

Easiest explanation: A circle can have only two parallel tangents. These two parallel tangents touch EITHER end of the diameter. Hence, ‘A circle can have only two parallel tangents’ is the only CORRECT statement.
Discussion
16.

The line intersecting a circle at exactly one point is called as _____(a) arc(b) secant(c) chord(d) tangentThe question was posed to me in an interview.Asked question is from Tangent to a Circle topic in portion Circles of Mathematics – Class 10

Answer»

The CORRECT answer is (d) tangent

Explanation: A line that touches/intersects a circle at exactly one point of a circle is CALLED a tangent and an infinite number of TANGENTS are drawn to a circle whereas secant is a line that intersects two DISTINCT POINTS on a circle.
Discussion
17.

How many tangents can be drawn at one point on a circle?(a) Only one(b) Three(c) Zero(d) TwoThis question was addressed to me at a job interview.The above asked question is from Number of Tangents from a Point on the Circle in division Circles of Mathematics – Class 10

Answer»

The correct ANSWER is (a) Only one

Best EXPLANATION: A CIRCLE is a set of points on a plane that is EQUIDISTANT from a fixed POINT and we can draw only one tangent at one point on any circle given.
Discussion
18.

How many tangents can a circle have?(a) Zero(b) Infinity(c) Estimated on the value of the radius(d) Fixed for every kind of circleI had been asked this question in an online quiz.This key question is from Number of Tangents from a Point on the Circle in section Circles of Mathematics – Class 10

Answer» CORRECT answer is (b) Infinity

Explanation: A CIRCLE is a set of points on a plane that is EQUIDISTANT from a FIXED point and an INFINITE number of tangents can be drawn for any given circle.
Discussion