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Four points on a circle

Source: BdMO 2024 Secondary National P2

March 18, 2024

geometrycyclic quadrilateralpower of a point

Problem Statement

In a cyclic quadrilateral

ABCD

, the diagonals intersect at

E

.

F

and

G

are on chord

AC

and chord

BD

respectively such that

AF = BE

and

DG = CE

. Prove that,

A, G, F, D

lie on the same circle.

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