MathDB
Problems
Contests
International Contests
Pan African
2002 Pan African
2
2
Part of
2002 Pan African
Problems
(1)
Perpendicular bisector passes through a point
Source: Pan Africa 2002
8/20/2005
△
A
O
B
\triangle{AOB}
△
A
OB
is a right triangle with
∠
A
O
B
=
9
0
o
\angle{AOB}=90^{o}
∠
A
OB
=
9
0
o
.
C
C
C
and
D
D
D
are moving on
A
O
AO
A
O
and
B
O
BO
BO
respectively such that
A
C
=
B
D
AC=BD
A
C
=
B
D
. Show that there is a fixed point
P
P
P
through which the perpendicular bisector of
C
D
CD
C
D
always passes.
geometry
circumcircle
perpendicular bisector