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CCA Math Bonanza
2022 CCA Math Bonanza
I5
I5
Part of
2022 CCA Math Bonanza
Problems
(1)
Early Timesink
Source:
4/26/2022
Let
Γ
1
\Gamma_1
Γ
1
be a circle with radius
5
2
\frac{5}{2}
2
5
.
A
A
A
,
B
B
B
, and
C
C
C
are points on
Γ
1
\Gamma_1
Γ
1
such that
A
B
‾
=
3
\overline{AB} = 3
A
B
=
3
and
A
C
‾
=
5
\overline{AC} = 5
A
C
=
5
. Let
Γ
2
\Gamma_2
Γ
2
be a circle such that
Γ
2
\Gamma_2
Γ
2
is tangent to
A
B
AB
A
B
and
B
C
BC
BC
at
Q
Q
Q
and
R
R
R
, and
Γ
2
\Gamma_2
Γ
2
is also internally tangent to
Γ
1
\Gamma_1
Γ
1
at
P
P
P
.
Γ
2
\Gamma_2
Γ
2
intersects
A
C
AC
A
C
at
X
X
X
and
Y
Y
Y
.
[
P
X
Y
]
[PXY]
[
PX
Y
]
can be expressed as
a
b
c
\frac{a\sqrt{b}}{c}
c
a
b
. Find
a
+
b
+
c
a+b+c
a
+
b
+
c
.2022 CCA Math Bonanza Individual Round #5