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?

8 cm

⇒ 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.