MathDB

Let

I

and

O

be the incenter and the circumcenter of a triangle

ABC

, respectively, and let

s_a

be the exterior bisector of angle

\angle BAC

. The line through

I

perpendicular to

IO

meets the lines

BC

and

s_a

at points

P

and

Q

, respectively. Prove that

IQ = 2IP

Problem Statement