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concyclic , intersecting circles (2018 Adygea Teachers' Geometry Olympiad p3)

Source:

June 22, 2020

geometryConcycliccircles

Problem Statement

Two circles intersect at points

A

and

B

. Through point

B

, a straight line intersects the circles at points

C

and

D

, and then tangents to the circles are drawn through points

C

and

D

. Prove that the points

A, D, C

and

P

- the intersection point of the tangents - lie on the same circle.