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\mathrm{AB} is a chord of the circle \mathrm{x}^{2}+\mathrm{y}^{2}=25. The tangents at \mathrm{A} and \mathrm{B} intersect at \mathrm{C}. If (2, 3 ) is the mid-point of \mathrm{A B}, the area of the quadrilateral \mathrm{OACB} is

Option: 1

50 \sqrt{\frac{13}{3}}


Option: 2

50 \sqrt{\frac{3}{13}}


Option: 3

50 \sqrt{3}


Option: 4

\frac{50}{\sqrt{13}}


Answers (1)

\text{Area }=\mathrm{OB} \times \mathrm{BC}=5^{2} \cot \theta

50 \sqrt{\frac{3}{13}}$, since $\sin \theta=\frac{\sqrt{13}}{5}

Posted by

Sumit Saini

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