In ` A B C ,l e tR=c i r c u m r a d i u s ,r=in r a d i u sdot` If `r` is the distance between the circumcenter and the incenter, the ratio `R/r` is equal to `sqrt(2)-1` (b) `sqrt(3)-1` `sqrt(2)+1` (d) `sqrt(3)+1`

Prove that the distance between the circumcenter and the incenter of triangle ABC is sqrt(R^2-2R r)

Prove that the distance between the circumcenter and the incenter of triangle ABC is sqrt(R^2-2R 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 , 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

If in triangle A B C ,sumsinA/2=6/5a n dsumI I_1=9 (where I_1,I_2a n dI_3 are excenters and I is incenter, then circumradius R is equal to (15)/8 (b) (15)/4 (c) (15)/2 (d) 4/(12)

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is (a) (2+sqrt(3))r (b) ((2+sqrt(3)))/(sqrt(3))r (c) ((2-sqrt(3)))/(sqrt(3))r (d) (2-sqrt(3))r

If the sides of a triangle are in G.P., and its largest angle is twice the smallest, then the common ratio r satisfies the inequality 0

The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (c) (3sqrt(3))/8R^2 (d) R^2

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

In any triangle, the minimum value of r_1r_2r_3//r^3 is equal to 1 (b) 9 (c) 27 (d) none of these