MathDB

equal circumcircles, parallelogram, cyclic (2011 Kyiv City MO 11.4)

Source:

July 15, 2020

geometrycircumcircleparallelogramequal circlescyclic quadrilateral

Problem Statement

On the diagonals

AC

and

BD

of the inscribed quadrilateral A

BCD

, the points

X

and

Y

are marked, respectively, so that the quadrilateral

ABXY

is a parallelogram. Prove that the circumscribed circles of triangles

BXD

and

CYA

have equal radii.
(Vyacheslav Yasinsky)