Mathematics

Mathematics

Problem

The area (in sq units) of the part of the circle x2+y2=169x^2 + y^2 = 169 which is below the line 5x−y=135x - y = 13 is πα2β−652+αβsin⁡−1(1213), where α,β are coprime\frac{\pi\alpha}{2\beta} - \frac{65}{2} + \frac{\alpha}{\beta} \sin^{-1} \left( \frac{12}{13} \right), \text{ where } \alpha, \beta \text{ are coprime} numbers. Then, α+β\alpha + \beta is equal to .... (2024 Main, 29 Jan I)

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