MathDB

Some geometry

Source: St Petersburg Olympiad 2010, Grade 10, P3

September 14, 2017

geometry

Problem Statement

M,N

are midpoints of

AB

and

CD

for convex quadrilateral

ABCD

. Points

X

and

Y

are on

AD

and

BC

and

XD=3AX,YC=3BY

\angle MXA=\angle MYB = 90

. Prove that

\angle XMN=\angle ABC