MathDB

Let

{ABC}

be an acute angled triangle whose shortest side is

{BC}

. Consider a variable point

{P}

on the side

{BC}

, and let

{D}

and

{E}

be points on

{AB}

and

{AC}

, respectively, such that

{BD=BP}

and

{CP=CE}

. Prove that, as

{P}

traces

{BC}

, the circumcircle of the triangle

{ADE}

passes through a fixed point.

Problem Statement