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Isogonal conjugate on (BIC)

Source: Kvant Magazine No. 5-6 2024 M2794

August 25, 2024

geometry

Problem Statement

The points

P

and

Q

lie inside the circle

\omega

. The perpendicular bisector to the segment

PQ

intersects

\omega

at points

A

and

D

. A circle centered on

D

passing through

P

and

Q

intersects

\omega

at points

B

and

C

. The segment

PQ

lies inside the triangle

ABC

. Prove that

\angle ACP = \angle BCQ

. Proposed by A. Zaslavsky

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