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Tangent Line.

Source: EGMO 2016 Day 1 Problem 2

April 12, 2016

geometrycyclic quadrilateraltangentmidpointsEGMOEGMO 2016

Problem Statement

Let

ABCD

be a cyclic quadrilateral, and let diagonals

AC

and

BD

intersect at

X

.Let

C_1,D_1

and

M

be the midpoints of segments

CX,DX

and

AC

, respecctively. Lines

BD

and

BC_1

intersect at

Y

, and line

MY

intersects diagonals

AC

and

BD

at different points

E

and

F

, respectively. Prove that line

XY

is tangent to the circle through

E,F

and

X

.

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