The length of the tangent to a circle from a point P is 15 cm. Point P is 17 cm away from the centre. What is the radius of the circle?
Answer & explanation
Correct answer: option 3
⇒ Let AP be the tangent and OA be the radius
Now,
AP = 15
OP = 17
As we know the radius makes \({90}^\circ\) at a tangent.
So,
⇒ \( {OA }^{2 } \) + \( {AP }^{2 } \) = \( {OP }^{2 } \)
⇒ \( {OA }^{2 } \) + \( {15 }^{2 } \) = \( {17 }^{2 } \)
⇒ \( {OA }^{2 } \) + 225 = 289
⇒ \( {OA }^{2 } \) = 64
⇒ OA = 8,
So, radius = 8 cm,
Therefore, the radius of the circle is 8 cm.