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2018 JHMT
3
3
Part of
2018 JHMT
Problems
(1)
2018 JHMT Geometry #3
Source:
9/5/2023
An equilateral triangle
A
B
C
ABC
A
BC
is in between two parallel lines
x
,
y
x, y
x
,
y
that pass through points
A
A
A
and
B
B
B
respectively. Given that
C
C
C
is twice as far from
y
y
y
as
x
x
x
, the acute angle that
C
A
CA
C
A
makes with
x
x
x
is
θ
\theta
θ
. Then
(
tan
θ
)
2
(\tan \theta)^2
(
tan
θ
)
2
is of 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
.
geometry