Let P be a point outside a circle Γ, and let the two tangent lines through P touch Γ at A and B. Let C be on the minor arc AB, and let ray PC intersect Γ again at D. Let ℓ be the line through B and parallel to PA. ℓ intersects AC and AD at E and F, respectively. Prove that B is the midpoint of EF. projective geometrygeometrycircumcirclegeometry unsolved