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Many angle conditions

Source: Oral Moscow geometry olympiad 2023 10-11.6

April 20, 2023

geometry

Problem Statement

Points

C_1

and

C_2

lie on side

AB

of triangle

ABC

, where the point

C_1

belongs to the segment

CC_1

and

CC_2

. On segments

CC_1

and

CC_2

points

A'

and

B'

are taken such that

\angle CAA'= \angle CBB' = \angle C_1CC_2

. Prove that the center of the circle

(CA'B')

lies on the perpendicular bisector of the segment

AB

.

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