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Internal tangent circles

Source: Kvant Magazine No. 3 2021 M2643

March 9, 2023

geometryKvant

Problem Statement

The circles

\omega

and

\Omega

touch each other internally at

A{}

. In a larger circle

\Omega

consider the chord

CD

which touches

\omega

at

B{}

. It is known that the chord

AB

is not a diameter of

\omega

. The point

M{}

is the middle of the segment

AB{}

. Prove that the circumcircle of the triangle

CMD

passes through the center of

\omega

.
Proposed by P. Bibikov

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