# Go back to 1950 for the answer

Geometry Level 5

$\large (1950\cos \alpha, 1950\sin \alpha) , \quad (1950\cos \beta, 1950\sin \beta) , \quad (1950\cos \gamma, 1950\sin \gamma)$

A triangle has vertices on the coordinates as described above, where $$\alpha,\beta$$ and $$\gamma$$ satisfy the following system of equations,

$\large \cos \alpha + \cos \beta + \cos \gamma = \dfrac{411}{325} , \qquad \sin \alpha + \sin \beta + \sin \gamma = \dfrac{872}{325}.$

If the orthocenter of this triangle has a coordinate of $$(a,b)$$, compute $$a+b$$.