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2023 AIME
3
similar triangles yay
similar triangles yay
Source: 2023 AIME II Problem #3
February 16, 2023
geometry
AIME
AIME II
Problem Statement
Let
△
A
B
C
\triangle{ABC}
△
A
BC
be an isoceles triangle with
∠
A
=
9
0
∘
\angle A=90^{\circ}
∠
A
=
9
0
∘
. There exists a point
P
P
P
inside
△
A
B
C
\triangle{ABC}
△
A
BC
such that
∠
P
A
B
=
∠
P
B
C
=
∠
P
C
A
\angle PAB=\angle PBC=\angle PCA
∠
P
A
B
=
∠
PBC
=
∠
PC
A
and
A
P
=
10
AP=10
A
P
=
10
. Find the area of
△
A
B
C
\triangle{ABC}
△
A
BC
.
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