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2 circles internally tangent to third one (2014 Kyiv City MO 9.3)

Source:

August 6, 2020

geometrycirclestangent circles

Problem Statement

Two circles

{{c} _ {1}}, \, \, {{c} _ {2}}

pass through the center

O

of the circle

c

and touch it internally in points

A

and

B

, respectively. Prove that the line

AB

passes though a common point of circles

{{c} _ {1}}, \, \, {{c} _ {2}}