This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 1

2024 CAPS Match, 3
Let $ABC$ be a triangle and $D$ a point on its side $BC.$ Points $E, F$ lie on the lines $AB, AC$ beyond vertices $B, C,$ respectively, such that $BE = BD$ and $CF = CD.$ Let $P$ be a point such that $D$ is the incenter of triangle $P EF.$ Prove that $P$ lies inside the circumcircle $\Omega$ of triangle $ABC$ or on it.
incenter circumcircle length geometry same interior