MathDB

Geometry

Source: Federal Mathematical Competition of Serbia and Montenegro 2004

May 14, 2018

geometry

Problem Statement

In a triangle

ABC

, points

D

and

E

are taken on rays

CB

and

CA

respectively so that

CD=CE = \frac{AC+BC}{2}

. Let

H

be the orthocenter of the triangle, and

P

be the midpoint of the arc

AB

of the circumcircle of

ABC

not containing

C

. Prove that the line

DE

bisects the segment

HP