MathDB

18th ibmo - argentina 2003/q2

Source: Spanish Communities

April 8, 2006

trigonometrygeometrytrapezoidcircumcircleradical axiscyclic quadrilateralpower of a point

Problem Statement

Let

C

and

D

be two points on the semicricle with diameter

AB

such that

B

and

C

are on distinct sides of the line

AD

. Denote by

M

,

N

and

P

the midpoints of

AC

,

BD

and

O_AO_B

respectively. Let

O_A

and

O_B

the circumcentres of the triangles

ACP

and

BDP

. Show that the lines

O_AO_B

and

MN

are parallel.

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