MathDB

2 projections and a chord's midpoint collinear wanted

Source: 2005 Oral Moscow Geometry Olympiad grades 10-11 p2

October 21, 2020

geometrycollineardiameter

Problem Statement

On a circle with diameter

AB

, lie points

C

and

D

XY

is the diameter passing through the midpoint

K

of the chord

CD

. Point

M

is the projection of point

X

onto line

AC

, and point

N

is the projection of point

Y

on line

BD

. Prove that points

M, N

and

K

are collinear.
(A. Zaslavsky)