MathDB

midpoint of XY lies on diagonal BD of square ABCD (2020 NZMO 1.2)

Source:

January 10, 2021

midpointsquaregeometry

Problem Statement

Let

ABCD

be a square and let

X

be any point on side

BC

between

B

and

C

. Let

Y

be the point on line

CD

such that

BX = YD

and

D

is between

C

and

Y

. Prove that the midpoint of

XY

lies on diagonal

BD