MathDB

Geometry

Source: Polish Mathematical Olympiad 2016 P6- Final Round

April 8, 2016

geometryincenterreflectiongeometric transformationperpendicular lines

Problem Statement

Let

I

be an incenter of

\triangle ABC

. Denote

D, \ S \neq A

intersections of

AI

with

BC, \ O(ABC)

respectively. Let

K, \ L

be incenters of

\triangle DSB, \ \triangle DCS

. Let

P

be a reflection of

I

with the respect to

KL

. Prove that

BP \perp CP