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Quadratic concurrence in circumscribed quad

Source: IOM 2018 #2, Géza Kós

September 6, 2018

geometryIOM

Problem Statement

A convex quadrilateral

ABCD

is circumscribed about a circle

\omega

. Let

DP

be the diameter of

\omega

perpendicular to

AC

. Suppose lines

BP

and

DQ

intersect at point

X

, and lines

BQ

and

DP

intersect at point

Y

. Show that the points

X

and

Y

lie on the line

AC

.
Géza Kós

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