Two tangents drawn from $\mathrm{P}(1,7)$ to the circle $x^2+y^2=25$, touch the circle at Q and R respectively. The area of the quadrilateral PQOR is

• A

  16 sq. units
• B

  36 sq. units
• Correct answer
  C

  25 sq. units
• D

  49 sq. units

Solution

Length of tangent segment from $\mathrm{P}(1,7)$ is $\begin{aligned} \sqrt{1^2+7^2-5^2} & =5 \\ \text { Required area } & =2 \times \text { Area of } \triangle \mathrm{PQO} \\ & =2 \times \frac{1}{2} \times 5 \times 5 \\ & =25 \text { sq. } \end{aligned}$

Hence, the correct answer is option: 'C'.