MathDB

2018 JHMT Geometry #3

Source:

September 5, 2023

geometry

Problem Statement

An equilateral triangle

ABC

is in between two parallel lines

x, y

that pass through points

A

and

B

respectively. Given that

C

is twice as far from

y

as

x

, the acute angle that

CA

makes with

x

is

p + q

. Then

(\tan \theta)^2

is of the form

\frac{p}{q}

where

p, q

are relatively prime positive integers. Find

p + q

.

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