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Familiar cyclic quad config

Source: India IMOTC Practice Test 1 Problem 2

May 31, 2024

geometry

Problem Statement

Let

ABCD

be a convex cyclic quadrilateral with circumcircle

\omega

. Let

BA

produced beyond

A

meet

CD

produced beyond

D

, at

L

. Let

\ell

be a line through

L

meeting

AD

and

BC

at

M

and

N

respectively, so that

M,D

(respectively

N,C

) are on opposite sides of

A

(resp.

B

). Suppose

K

and

J

are points on the arc

AB

of

\omega

not containing

C,D

so that

MK, NJ

are tangent to

\omega

. Prove that

K,J,L

are collinear.
Proposed by Rijul Saini

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