In an acute triangle △ABC, AB<AC<BC, and A1,B1,C1 are the projections of A,B,C to the corresponding sides. Let the reflection of B1 wrt CC1 be Q, and the reflection of C1 wrt BB1 be P.
Prove that the circumcirle of A1PQ passes through the midpoint of BC. geometrygeometric transformationreflectioncircumcircle