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Locus of circumcentres

Source: Tuymaada 2023 Junior P8

July 7, 2023

geometry

Problem Statement

Circle

\omega

lies inside the circle

\Omega

and touches it internally at point

P

. Point

S

is taken on

\omega

and the tangent to

\omega

is drawn through it. This tangent meets

\Omega

at points

A

and

B

. Let

I

be the centre of

\omega

. Find the locus of circumcentres of triangles

AIB

.

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