Distance Between Circumcenter and incenter

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

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

What is the Distance between circumcenter and orthocenter?

What is the Distance between Incenter and excenter?

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 DeltaABC , let R = circumradius, r= inradius. If r is the distance between the circumcenter and the incenter, then ratio R/r is equal to

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