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 \(a+b\).

Give your answer to 2 decimal places.


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