Let ABC be a triangle with circumcentre O and circumcircle Ω. Γ is the circle passing through O,B and tangent to AB at B. Let Γ intersect Ω a second time at P=B. The circle passing through P,C and tangent to AC at C intersects with Γ at M. Prove that ∣MP∣=∣MC∣. JBMOJBMO Shortlistgeometry