Two circles pass through points $A$ and $B$. A third circle touches both these circles and meets $AB$ at points $C$ and $D$. Prove that the tangents to this circle at these points are parallel to the common tangents of two given circles. Proposed by A.Zaslavsky
Problem
Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-13 (Grade-9-11)
Tags: geometry