If the area of the quadrilateral formed by the tangents from the origin to the circle $x^{2} + y^{2}

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If the area of the quadrilateral formed by the tangents from the origin to the circle $x^{2} + y^{2} + 6x - 10y + c = 0$ and the radii corresponding to the points of contact is 15 , then a value of $c$ is:

Accepted Answer

[Key Concept: Tangents from the origin + the two radii form a kite of area (tangent length)$	imes$radius; tangent length $= \sqrt{S_{1}}$.]Area of quadrilateral$$15 = \sqrt{34 - C}\sqrt{C}$$$$\begin{matrix} & C^{2} - 34C + 225 = 0 \ & \ (C - 25)(C - 9) = 0 \ & C = 9,25 \end{matrix}$$

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