MathDB

Nice Quadrilateral Geo

Source: 2021 ISL G4

July 12, 2022

ISL 2021IMO Shortlistgeometrycyclic quadrilateralconcurrency

Problem Statement

Let

ABCD

be a quadrilateral inscribed in a circle

\Omega.

Let the tangent to

\Omega

at

\overline{TE}\parallel\overline{CD}

meet rays

BA

and

BC

at

E

and

F,

respectively. A point

T

is chosen inside

\triangle ABC

so that

\overline{TE}\parallel\overline{CD}

and

\overline{TF}\parallel\overline{AD}.

Let

K\ne D

be a point on segment

DF

satisfying

TD=TK.

Prove that lines

AC,DT,

and

BK

are concurrent.

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