MathDB

Geometry from Izho(P3)

Source: International Zhautykov Olympiad

January 11, 2019

geometry

Problem Statement

Triangle

ABC

is given. The median

CM

intersects the circumference of

ABC

in

N

.

AN

and

Q

are chosen on the rays

CA

and

PM

respectively, such that

QM

is parallel to

PY

and

QM

is parallel to

AN

. Points

X

and

Y

are chosen on the segments

PM

and

QM

respectively, such that both

PY

and

QX

touch the circumference of

ABC

. Let

Z

be intersection of

PY

and

QX

. Prove that, the quadrilateral

MXZY

is circumscribed.

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