10th Class
Mathematics
Circles
Question Bank
Circle
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.