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four points concyclic

Source: 45th International Tournament of Towns, Senior A-Level P5, Fall 2023

December 11, 2023

geometry

Problem Statement

Chord

D E

of the circumcircle of the triangle

Q

intersects sides

A B

and

B C

in points

P

and

Q

respectively. Point

P

lies between

D

and

Q

. Angle bisectors

D F

and

E G

are drawn in triangles

A D P

and

Q E C

. It turned out that the points

D

,

F, G, E

are concyclic. Prove that the points

A, P, Q, C

are concyclic. Azamat Mardanov

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