`A B C` is an equilateral triangle of side `4c mdot` If `R , r, a n d,h` are the circumradius, inradius, and altitude, respectively, then `(R+r)/h` is equal to (a) 4 (b) 2 (c) 1 (d) 3

In an equilateral triangle , R:r:r_2 is equal to

In a triangle ABC, angleC=90^@, r and R are the inradius and circumradius of the triangle ABC respectively, then 2(r+R) is equal to

In the triangle ABC, if a=5, b=7 and c=3, find the angle B and the circumradius R.

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to a+b (b) b+c c+a (d) a+b+c

In triangle A B C , if cosA+cosB+cosC=7/4, t h e n R/r is equal to 3/4 (b) 4/3 (c) 2/3 (d) 3/2

In triangle A B C , if r_1=2r_2=3r_3, then a : b is equal to 5/4 (b) 4/5 (c) 7/4 (d) 4/7

In acute angled triangle A B C ,A D is the altitude. Circle drawn with A D as its diameter cuts A Ba n dA Ca tPa n dQ , respectively. Length of P Q is equal to /(2R) (b) (a b c)/(4R^2) 2RsinAsinBsinC (d) Δ /R

Let ABC be a triangle having O and I as its circumcentre and incentre, respectively. If R and r are the circumradius and the inradius respectively, then prove that (IO) 2 =R 2 −2Rr. Further show that the triangle BIO is right angled triangle if and only if b is the arithmetic mean of a and c.

Given an isoceles triangle with equal side of length b and angle alpha lt pi//4 , then the circumradius R is given by

For triangle ABC,R=5/2 and r=1. Let I be the incenter of the triangle and D,E and F be the feet of the perpendiculars from I->BC,CA and AB, respectively. The value of (ID*IE*IF)/(IA*IB*IC) is equal to (a) 5/2 (b) 5/4 (c) 1/10 (d) 1/5