# From AutoMATHic

Geometry Level 4

Let the point $$(x,y)$$ be a point along the unit circle $$x^2+y^2=1$$ in the first quadrant and $$\theta$$ be the angle measured counterclockwise from the positive $$x$$-axis such that $$\theta = \cos^{-1} \left( \dfrac{4x+3y}5 \right)$$.

If $$\tan \theta = \dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find the value of $$a^2+b^2$$.

×