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Parallel through Random points yield cyclic quadrilateral

Source: Netherlands IMO TST #1 2019 P4

July 16, 2019

parallelgeometrycyclic quadrilateralcircumcircle

Problem Statement

Let

\Delta ABC

be a scalene triangle. Points

D,E

lie on side

\overline{AC}

in the order,

A,E,D,C

. Let the parallel through

E

to

BC

intersect

\odot (ABD)

at

F

, such that,

E

and

F

lie on the same side of

AB

. Let the parallel through

E

to

AB

intersect

\odot (BDC)

at

G

, such that,

E

and

G

lie on the same side of

BC

. Prove, Points

D,F,E,G

are concyclic

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