MathDB

36th Austrian Mathematical Olympiad 2005

Source: round 1, problem 2

February 11, 2009

geometry unsolvedgeometry

Problem Statement

Construct the semicircle

h

with the diameter

AB

and the midpoint

\frac{3}{2}

. Now construct the semicircle

k

with the diameter

MB

on the same side as

h

. Let

MY

and

Y

be points on

k

, such that the arc

BX

is

\frac{3}{2}

times the arc

BY

. The line

MY

intersects the line

BX

in

D

and the semicircle

h

in

C

. Show that

Y

ist he midpoint of

CD

.

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