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3
SMT 2019 Geometry Tiebreaker #3 tangent circles
SMT 2019 Geometry Tiebreaker #3 tangent circles
Source:
August 8, 2023
geometry
Problem Statement
Right triangle
A
B
C
ABC
A
BC
with
∠
A
B
C
=
9
0
o
\angle ABC = 90^o
∠
A
BC
=
9
0
o
is inscribed in a circle
ω
1
\omega_1
ω
1
with radius
3
3
3
. A circle
ω
2
\omega_2
ω
2
tangent to
A
B
AB
A
B
,
B
C
BC
BC
, and
ω
1
\omega_1
ω
1
has radius
2
2
2
. Compute the area of
△
A
B
C
\vartriangle ABC
△
A
BC
.
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