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National and Regional Contests
China Contests
China National Olympiad
2022 China National Olympiad
1
1
Part of
2022 China National Olympiad
Problems
(1)
Locus of incenter of quadrilateral
Source: CMO 2022 P1
12/21/2021
Let
a
a
a
and
b
b
b
be two positive real numbers, and
A
B
AB
A
B
a segment of length
a
a
a
on a plane. Let
C
,
D
C,D
C
,
D
be two variable points on the plane such that
A
B
C
D
ABCD
A
BC
D
is a non-degenerate convex quadrilateral with
B
C
=
C
D
=
b
BC=CD=b
BC
=
C
D
=
b
and
D
A
=
a
DA=a
D
A
=
a
. It is easy to see that there is a circle tangent to all four sides of the quadrilateral
A
B
C
D
ABCD
A
BC
D
. Find the precise locus of the point
I
I
I
.
geometry