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Geometry in Taiwan TST

Source: 2024 Taiwan TST Round 1 Independent Study 2-G

March 7, 2024

geometry

Problem Statement

For the quadrilateral

ABCD

, let

AC

and

BD

intersect at

E

,

AB

and

CD

intersect at

F

, and

AD

and

BC

intersect at

G

. Additionally, let

W, X, Y

, and

Z

be the points of symmetry to

E

with respect to

AB, BC, CD,

and

DA

respectively. Prove that one of the intersection points of

\odot(FWY)

and

\odot(GXZ)

lies on the line

FG

.
Proposed by chengbilly

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