question_answer

In figure, there are two concentric circles, with centre O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP == 12 cm, find the length of BP.

A) 12 cm             

B)        \[12.65\text{ }cm\]                 

C)        \[12.36\,cm\]               

D)        \[12.56\,cm\]               

Correct Answer: B

Solution :

\[PA=12cm,\]        \[OA=5\text{ }cm,\]             \[OB=3\text{ }cm,\]            \[O{{P}^{2}}=O{{A}^{2}}+A{{P}^{2}}\] \[=O{{B}^{2}}+B{{P}^{2}}\]             \[\Rightarrow \]            \[25+144=9+B{{P}^{2}}\] \[\Rightarrow \]     \[BP=\sqrt{160}\,cm=12.65\,cm\]   (approx.)