MathDB

Bosnia and Herzegovina EGMO TST 2017 Problem 2

Source: Bosnia and Herzegovina EGMO Team Selection Test 2017

September 19, 2018

geometrycircumcircleangle bisector

Problem Statement

It is given triangle

ABC

and points

P

and

Q

on sides

AB

and

AC

, respectively, such that

PQ\mid\mid BC

. Let

X

and

Y

be intersection points of lines

BQ

and

CP

with circumcircle

k

of triangle

APQ

, and

D

and

E

intersection points of lines

AX

and

AY

with side

BC

. If

2\cdot DE=BC

, prove that circle

k

contains intersection point of angle bisector of

\angle BAC

with

BC