# Constant Distance of Trig Points

Geometry Level 4

The distance between the points $\left(\dfrac{\sqrt{3}}{2}\sin (\alpha-c), \dfrac{1}{2}\sin(\alpha-c)\right)$ $\left(\dfrac{1}{2}\sin (\alpha+c), \dfrac{\sqrt{3}}{2}\sin(\alpha+c)\right)$

is constant, for some constant $$c$$ and variable $$\alpha$$.

If the distance between the points can be expressed as $$\dfrac{p}{q}$$ for positive coprime integers $$p,q$$, then find $$p+q$$.

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