Problem

Source: Brazilian Mathematical Olympiad 2023, Level 3, Problem 2

Tags: geometry, right triangle, Equilateral Triangle



Let ABC be a right triangle in B, with height BT, T on the hypotenuse AC. Construct the equilateral triangles BTX and BTY so that X is in the same half-plane as A with respect to BT and Y is in the same half-plane as C with respect to BT. Point P is the intersection of AY and CX. Show that PABC=PBCA=PCAB.