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

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) a+b (b) b+c (c) c+a (d) a+b+c

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 an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio a)2:4:5 (b) 1:2:3 (c) 1:2:4 (d) 2:4:3

Let A B C be a triangle having O and I as its circumcenter and incentre, respectively. If R and r are the circumradius and the inradius, respectively, then prove that (O I)^2=R^2-2R rdot Further show that the triangle B I O is a right angled triangle if and only if b is arithmetic mean of a and c.

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

In a triangle with sides a,b,c,r_1 gt r_2 gt r_3 ( which are the ex - radii ) then

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) (c) 2RsinAsinBsinC (d) delta/R

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

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