question_answer

Tangents are drawn to a circle of radius R from an external point P, to touch the circle at A and B. If C is centre of the circle and mid-point of AB is Q, then the value of \[CP\cdot CQ\] is

A) \[\frac{{{R}^{2}}}{2}\]                  

B) \[{{R}^{2}}\]

C) \[\frac{3{{R}^{2}}}{2}\]    

D) \[4{{R}^{2}}\]

Correct Answer: B

Solution :

[b] \[\tan \theta =\frac{R}{L}\] \[CP.CQ=\left( \sqrt{{{R}^{2}}+{{L}^{2}}} \right)\times R\sin \theta \] \[=\left( \sqrt{{{R}^{2}}+{{L}^{2}}} \right)\times R\times \frac{R}{\sqrt{{{R}^{2}}+{{L}^{2}}}}={{R}^{2}}\]