Let BC be a fixed segment in the plane, and let A be a variable point in the plane not on the line BC. Distinct points X and Y are chosen on the rays CA→ and BA→, respectively, such that ∠CBX=∠YCB=∠BAC. Assume that the tangents to the circumcircle of ABC at B and C meet line XY at P and Q, respectively, such that the points X, P, Y and Q are pairwise distinct and lie on the same side of BC. Let Ω1 be the circle through X and P centred on BC. Similarly, let Ω2 be the circle through Y and Q centred on BC. Prove that Ω1 and Ω2 intersect at two fixed points as A varies.Daniel Pham Nguyen, Denmark geometryfixed pointssymmetrymoving pointsRMMrmm 2024