MathDB

In triangle

ABC

let

O

and

H

be the circumcenter and the orthocenter. The point

P

is the reflection of

A

with respect to

OH

. Assume that

P

is not on the same side of

BC

A

. Points

E,F

lie on

AB,AC

respectively such that

BE=PC \ , CF=PB

. Let

K

be the intersection point of

AP,OH

. Prove that

\angle EKF = 90 ^{\circ}

Proposed by Iman Maghsoudi

Problem Statement