question_answer

The length of a tangent from a point A at distance 10 cm from the centre of the circle is 8 cm. Find the radius of the circle.

A)  2 cm                           

B)  4 cm       

C)  6 cm  

D)  8 cm

Correct Answer: C

Solution :

(c): Given, OP = 10 cm and AM = 8 cm (let M be point of contact for Tangney) \[\because \] \[OM\bot LAM\] (\[\because \] Radius is perpendicular to AM) In right \[\Delta \,OMA,\text{ }O{{A}^{2}}=O{{M}^{2}}+M{{A}^{2}}\] \[\Rightarrow \] \[{{10}^{2}}=O{{M}^{2}}+{{8}^{2}}\] \[\Rightarrow \] \[O{{M}^{2}}=100-64=36\] \[\Rightarrow \] \[OM=6cm\] Hence, radius of the circle is 6 cm.