P13

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

Tangents parallel to tangents

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-13 (Grade-9-11)

Two circles pass through points

A

B

. A third circle touches both these circles and meets

AB

C

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