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concyclic wanted , 2 diameters, 3 circles related

Source: Indonesia INAMO Shortlist 2017 G8 https://artofproblemsolving.com/community/c1101409_indonesia_shortlist__geometry

November 15, 2021

Concyclicgeometry

Problem Statement

Given a circle centered at point

O

, with

AB

as the diameter. Point

D

lies on the extension of line

C

so that

B

lies between

A

and

C

, and the line through

C

intersects the circle at points

D

and

E

(where

D

lies between

C

and

E

).

OF

is the diameter of the circumcircle of triangle

OBD

, and the extension of the line

CF

intersects the circumcircle of triangle

OBD

at point

G

. Prove that the points

O, A, E, G

lie on a circle.

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