A point P is 13 cm from the centre of a circle. The length of the tangent drawn from P to the circle is 12 cm. Find the distance of P from the nearest point of the circle.

Let T be the point of contact of the tangent from point P to the circle with centre O.

From figure,

OT ⊥ PT (As tangent and radius from point of contact are perpendicular to each other.)

In right-angled triangle OPT

⇒ OP² = OT² + PT²
⇒ 13² = OT² + 12²
⇒ 169 - 144 = OT²
⇒ OT² = 25
⇒ OT = 5 cm.

From figure,

⇒ OA = OT = 5 cm (Radius of the circle.)

⇒ PA = OP - OA = 13 - 5 = 8 cm.

Hence, the distance of P from the nearest point of circle = 8 cm.