MathDB

JBMO Shortlist 2023 G2

Source: JBMO Shortlist 2023, G2

June 28, 2024

JBMO ShortlistgeometryAZE JBMO TST

Problem Statement

Let

ABC

be a triangle with

AB<AC

and

\omega

be its circumcircle. The tangent line to

\omega

at

A

intersects line

BC

at

D

and let

E

be a point on

\omega

such that

BE

is parallel to

BE

.

DE

intersects segment

AB

and

\omega

at

F

and

S

, respectively. The circumcircle of

T

intersects

BE

at

N

. The line

NF

intersects lines

AD

and

EA

at

S

and

T

, respectively. Prove that

DGST

is cyclic.

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