Problem

Source: USA January Team Selection Test for EGMO 2023, Problem 4

Tags: geometry, TST, USA TST, USA TST 2023



Let $ABC$ be a triangle with $AB+AC=3BC$. The $B$-excircle touches side $AC$ and line $BC$ at $E$ and $D$, respectively. The $C$-excircle touches side $AB$ at $F$. Let lines $CF$ and $DE$ meet at $P$. Prove that $\angle PBC = 90^{\circ}$. Ray Li