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concyclic , given cyclic quad

Source: Polish MO second round 1969 p3

August 28, 2024

geometryConcyclicCyclic

Problem Statement

Given a quadrilateral

ABCD

inscribed in a circle. The images of the points

A

and

C

in symmetry with respect to the line

B'

are the points

A'

and

C'

, respectively, and the images of the points

B

and

D

in symmetry with respect to the line

AC

are the points

B'

and

D'

respectively. Prove that the points

A'

,

B'

,

C'

,

D'

lie on the circle.

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