In triangle ABC the midpoint of BC is called M. Let P be a variable interior point of the triangle such that ∠CPM=∠PAB. Let Γ be the circumcircle of triangle ABP. The line MP intersects Γ a second time at Q. Define R as the reflection of P in the tangent to Γ at B. Prove that the length ∣QR∣ is independent of the position of P inside the triangle. geometrycircumcirclegeometric transformationreflectiontrapezoidgeometry proposed