MathDB

AB,CD,XY concurrent or //, cyclic, circumcircle (Kharkiv City XI 2017- Ukr)

Source:

March 19, 2020

geometryKharkivcirclesconcurrencycircumcircleCyclic

Problem Statement

The quadrilateral

ABCD

is inscribed in the circle

\omega

. Lines

AD

and

BC

intersect at point

E

. Points

M

and

N

are selected on segments

AD

and

BC

, respectively, so that

AM: MD = BN: NC

. The circumscribed circle of the triangle

EMN

intersects the circle

\omega

at points

X

and

Y

. Prove that the lines

AB, CD

and

XY

intersect at the same point or are parallel.