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Romania TST 2021 Day 2 P3

Source:

June 13, 2021

geometryquadrilateralromaniaRomanian TSTTST

Problem Statement

Let

\mathcal{P}

be a convex quadrilateral. Consider a point

X

inside

\mathcal{P}.

Let

M,N,P,Q

be the projections of

X

on the sides of

\mathcal{P}.

We know that

M,N,P,Q

all sit on a circle of center

L.

Let

J

and

K

be the midpoints of the diagonals of

\mathcal{P}.

Prove that

J,K

and

L

lie on a line.

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