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1990 IMO Longlists
90
90
Part of
1990 IMO Longlists
Problems
(1)
Find the locus of the incenter - ILL 1990 TUR1
Source:
9/19/2010
Let
P
P
P
be a variable point on the circumference of a quarter-circle with radii
O
A
,
O
B
OA, OB
O
A
,
OB
and
∠
A
O
B
=
9
0
∘
\angle AOB = 90^\circ
∠
A
OB
=
9
0
∘
. H is the projection of
P
P
P
on
O
A
OA
O
A
. Find the locus of the incenter of the right-angled triangle
H
P
O
.
HPO.
H
PO
.
geometry
incenter
circumcircle
geometry proposed