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2020 ASDAN Math Tournament
13
13
Part of
2020 ASDAN Math Tournament
Problems
(1)
2020 Team #13
Source:
10/24/2023
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral such that
△
A
B
C
\vartriangle ABC
△
A
BC
is an equilateral triangle. Let
P
P
P
be a point inside the quadrilateral such that
△
A
P
D
\vartriangle APD
△
A
P
D
is an equilateral triangle and
∠
P
C
D
=
3
0
o
\angle PCD = 30^o
∠
PC
D
=
3
0
o
. Suppose
C
P
=
6
CP = 6
CP
=
6
and
C
D
=
8
CD = 8
C
D
=
8
. The area of the triangle formed by
P
P
P
, the midpoint of
B
C
‾
\overline{BC}
BC
, and the midpoint of
A
B
‾
\overline{AB}
A
B
can be expressed in simplest radical form as
a
+
b
c
d
\frac{a+b\sqrt{c}}{d}
d
a
+
b
c
, where
a
a
a
,
b
b
b
,
c
c
c
, and
d
d
d
are positive integers with
g
c
d
(
a
,
b
,
d
)
=
1
gcd(a, b, d) = 1
g
c
d
(
a
,
b
,
d
)
=
1
and with
c
c
c
not divisible by the square of any prime. Compute
a
+
b
+
c
+
d
a + b + c + d
a
+
b
+
c
+
d
.
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