MathDB

Poland 2017 P5

Source:

April 4, 2017

geometry

Problem Statement

Point

M

is the midpoint of

BC

of a triangle

ACD

, in which

AB=AC

. Point

D

is the orthogonal projection of

M

on

AB

. Circle

\omega

is inscribed in triangle

ACD

and tangent to segments

AD

and

AC

at

K

and

L

respectively. Lines tangent to

\omega

which pass through

M

cross line

KL

at

X

and

Y

, where points

X

,

K

,

L

and

Y

lie on

KL

in this specific order. Prove that points

M

,

D

,

X

and

Y

are concyclic.

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