Quadrangle ABCD is inscribed in a circle. The perpendicular from the vertex C on the bisector of ∠ABD intersects the line AB at the point C1. The perpendicular from the vertex B on the bisector of ∠ACD intersects the line CD at the point B1. Prove that B1C1∥AD.
Problem
Source: 2010 Oral Moscow Geometry Olympiad grades 10-11 p2
Tags: geometry, cyclic quadrilateral, perpendicular, parallel