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2000 Korea Junior Math Olympiad
7
2000 KJMO P7 Bashing Geometry
2000 KJMO P7 Bashing Geometry
Source: 2000 KJMO
June 30, 2024
geometry
computational geometry
KJMO
Problem Statement
A
B
C
ABC
A
BC
is a triangle that
2
∠
B
<
∠
A
<
9
0
∘
2\angle B < \angle A <90^{\circ}
2∠
B
<
∠
A
<
9
0
∘
, and
P
P
P
is a point on
A
B
AB
A
B
satisfying
∠
A
=
2
∠
A
P
C
\angle A=2\angle APC
∠
A
=
2∠
A
PC
. If
B
C
=
a
BC=a
BC
=
a
,
A
C
=
b
AC=b
A
C
=
b
,
B
P
=
1
BP=1
BP
=
1
, express
A
P
AP
A
P
as a function of
a
,
b
a, b
a
,
b
.
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