PA and PB are tangents to the circle and O is the centre of the circle. The radius is 5 cm and PO is 13 cm. If the area of the triangle PAB is M, value of M15 is :

PA and PB are tangents to the circle and O is the centre of the circle. The radius is 5 cm and PO is 13 cm. If the area of the triangle PAB is M, value of $$\sqrt{\frac{\text{M}}{15}}$$ is :

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& PA=12\text{ cm}\\ & \sin \theta =\frac{AC}{AP}=\frac{AO}{OP}\\ & \frac{AC}{12}=\frac{5}{13}\\ & AC=\frac{60}{13}\\ & \tan \theta =\frac{AC}{PC}=\frac{AO}{AP}\\ & \frac{\frac{60}{13}}{PC}=\frac{5}{12}\\ & PC=\frac{144}{13}\\ & \text{Area of }\Delta PCB=\frac{1}{2}\times PC\times AC\\ & \text{Area of }\Delta PAB=PC\times AC\\ & M=\frac{144}{13}\times \frac{60}{13}\\ & \frac{\sqrt{M}}{15}=\sqrt{\frac{144\times 60}{13\times 13\times 15}}=\frac{24}{13}\end{array}$$