MathDB

Perpendicular bisector passes through a point

Source: Pan Africa 2002

August 20, 2005

geometrycircumcircleperpendicular bisector

Problem Statement

\triangle{AOB}

is a right triangle with

\angle{AOB}=90^{o}

.

C

and

D

are moving on

AO

and

BO

respectively such that

AC=BD

. Show that there is a fixed point

P

through which the perpendicular bisector of

CD

always passes.

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