MathDB

collinear wanted, semicircle related

Source: 1998 Estonia National Olympiad Final Round grade 10 p2

March 11, 2020

collineargeometrysemicircle

Problem Statement

Let

C

and

D

be two distinct points on a semicircle of diameter

AB

. Let

E

be the intersection of

AC

and

BD

F

be the intersection of

AD

and

BC

and

X, Y

, and

Z

are the midpoints of

AB, CD

, and

EF

, respectively. Prove that the points

X, Y,

and

Z

are collinear.