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 orthocentre of triangle ABC is Rsqrt(1-8cosAcosBcosC)

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

In a triangle ABC,r=

If R be the circum radius and r the in radius of a triangle ABC, show that Rge2r

Prove that the distance of the incentre of Delta ABC from A is 4R sin B/2 sin C/2.

Given an isoceles triangle with equal side of length b and angle alpha lt pi//4 , then the distance between circumcenter O and incenter I is

In triangle ABC, the line joining the circumcenter and incenter is parallel to side BC, then cosA+cosC is equal to -1 (b) 1 (c) -2 (d) 2

In triangle ABC, the line joining the circumcenter and incenter is parallel to side AC, then cos A + cos C is equal to

If R and R' are the circumradii of triangles ABC and OBC, where O is the orthocenter of triangle ABC, then :

If R and R' are the circumradii of triangles ABC and OBC, where O is the orthocenter of triangle ABC, then :