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in a quadrilateral with 2 opposite angles right ... a line bisects a segment

Source: 2014 Sharygin Geometry Olympiad Final Round 9.2

August 3, 2018

circlesgeometry

Problem Statement

In a quadrilateral

ABCD

angles

A

and

C

are right. Two circles with diameters

AB

and

CD

meet at points

X

and

Y

. Prove that line

XY

passes through the midpoint of

AC

.
(F. Nilov )