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MK is equal and perpendicular to the diagonal of the rectangle ABCD

Source: 2011 Oral Moscow Geometry Olympiad grades 8-9 p1

April 17, 2020

geometryrectangleequal segmentsperpendicular

Problem Statement

The bisector of angle

B

and the bisector of external angle

D

of rectangle

ABCD

intersect side

AD

and line

AB

at points

M

and

K

, respectively. Prove that the segment

MK

is equal and perpendicular to the diagonal of the rectangle.