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2018 JHMT
9
2018 JHMT Geometry #9
2018 JHMT Geometry #9
Source:
September 5, 2023
geometry
Problem Statement
In a trapezoid
A
B
C
D
ABCD
A
BC
D
,
A
D
∥
B
C
AD \parallel BC
A
D
∥
BC
and
∠
A
=
6
0
o
\angle A = 60^o
∠
A
=
6
0
o
. Let
E
E
E
be a point on
A
B
AB
A
B
, and let
O
1
O_1
O
1
and
O
2
O_2
O
2
be circumcenters of
△
A
E
D
\vartriangle AED
△
A
E
D
and
△
B
E
C
\vartriangle BEC
△
BEC
, respectively. Let
O
1
O
2
‾
D
C
‾
\frac{\overline{O_1O_2}}{\overline{DC}}
D
C
O
1
O
2
be
x
x
x
.
x
2
x^2
x
2
is in the form
p
q
\frac{p}{q}
q
p
where
p
,
q
p, q
p
,
q
are relatively prime positive integers. Find
p
+
q
p + q
p
+
q
.
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