MathDB

Let

M{}

be the midpoint of the side

BC

of the triangle

ABC

. The circle

\omega

passes through

A{}

, touches the line

BC

M{}

, intersects the side

AB

at the point

D{}

and the side

AC

at the point

E{}

. Let

X{}

and

Y{}

be the midpoints of

BE

and

CD

respectively. Prove that the circumcircle of the triangle

MXY

touches

\omega

.
Alexey Doledenok

Problem Statement