Related InterviewSolutions

• Let ABC be a triangle in which the line joining the circumecentre and incentre is parallel to base BC of the triangle. Then answer the following questions : If ODEI is a square where O and I stands for circumcentre and incentre, respectively and D and E are the point of perpendicular from O and I on the base BC, thenA. `(r )/(R )=(3)/(8)`B. `(r )/(R )=2-sqrt(3)`C. `(r )/(R )=sqrt(2)-1`D. `(r )/(R )=(1)/(4)`
• In `Delta ABC, a^(2)(s-a)+b^(2)(s-b)+c^(2)(s-c)=`A. `4R Delta(cos A+sin B+cos C)`B. `4R Delta(sin A+sin B+sin C)`C. `4R Delta(1+4sin.(A)/(2)sin.(B)/(2)sin.(C )/(2))`D. none of these
• In any `Delta ABC` line joiningcircumcentre (O) and incentre (I) is parallel to AC, then OI is equal toA. `R|tan((A-C)/(2))|`B. `R|tan(A-C)|`C. `R|sec((A-C)/(2))|`D. `R|sec(A-C)|`
• In a `Delta ABC`, if `tan.(A)/(2)=(5)/(6), tan.(B)/(2)=(20)/(37)`, then which of the following is/are correct ?A. `angle B gt angle C`B. `angle B lt angle C`C. `a gt b gt c`D. `a lt b lt c`
• In a triangle `ABC` if `cot(A/2)cot(B/2)=c, cot(B/2)cot(C/2)=a ` and `cot(C/2)cot(A/2)=b` then `1/(s-a)+1/(s-b)+1/(s-c)=`A. `-1`B. 0C. 1D. 2
• In `Delta ABC`, circumrdius is 3 inradius is 1.5 units. The value of a `acot^(2)A+b^(2)cot^(3)B+c^(3)cot^(4)C` isA. `13 sqrt(3)`B. `11sqrt(6)`C. 21D. none of these
• In `Delta ABC if tan(A/2) tan(B/2) + tan(B/2) tan(C/2) = 2/3 ` then `a+c`A. 3bB. 2bC. 3b/2D. 4b
• In the ambiguous case if the remaining angles of a triangle with given a, b, A and `B_(1),B_(2),C_(1),C_(2)` then `(sin C_(1))/(sin B_(1))+(sin C_(2))/(sin B_(2))=`A. 2 cos AB. 2 sin BC. 2 tan AD. 2 cot A
• The perimeter of a triangle ABC right angled at C is 70 and the inradius is 6, then `|a-b|=`A. 1B. 2C. 8D. 9
• In `Delta ABC` if `r_1=2r_2=3r_3` and `D` is the mid point of `BC` then `cos/_ADC=`A. `(7)/(25)`B. `-(7)/(25)`C. `(24)/(25)`D. `-(24)/(25)`