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fixed point for a circle, tangent to a given line

Source: 2016 Oral Moscow Geometry Olympiad grades 10-11 p5

July 29, 2019

geometryFixed pointfixedtangent

Problem Statement

From point

A

to circle

\omega

tangent

AD

and arbitrary a secant intersecting a circle at points

B

and

C

(B lies between points

A

and

C

). Prove that the circle passing through points

C

and

D

and touching the straight line

BD

, passes through a fixed point (other than

D