Question

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

• A. 6cm
• B. 5cm
• C. 10cm
• D. 7cm

Answer 1

The correct option is B

5cm

Since tangent at a point on the circle is perpendicular to the radius through the point.

$\therefore$ $\angle$OTP = ${90}^{\circ }$

In right angled triangle OTP

${OP}^2$ = ${OT}^2$ + ${PT}^2$ (By Pythagoras theorem)

${13}^2$ = ${OT}^2$ + ${12}^2$

169 = ${OT}^2$ + 144

${OT}^2$ = 169 - 144 = 25

PT = $\sqrt{25}$ = 5

Hence, radius of circle is 5 cm.