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Circles (OCD) touching a fixed circle

Source: Tuymaada 2023 Senior P4

July 7, 2023

geometry

Problem Statement

Two points

A

and

B

and line

\ell

are fixed in the plane so that

\ell

is not perpendicular to

AB

and does not intersect the segment

AB

. We consider all circles with a centre

O

not lying on

\ell

, passing through

A

and

B

and meeting

\ell

at some points

C

and

D

. Prove that all the circumcircles of triangles

OCD

touch a fixed circle.

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