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.

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Answer 1

Since tangent to a circle is perpendictflar to the radius through the point of contact.
$\angle$OTP = ${90}^0$

In right triangle OTP

$\Rightarrow$ ${OP}^2$ = ${OT}^2$ + ${PT}^2$
$\Rightarrow$${13}^2$ = ${OT}^2$ + ${12}^2$
$\Rightarrow$${OT}^2$ = 169 - 144 = 25
$\Rightarrow$${OT}^2$ = 25
OT = $\sqrt{25}$= 5 cm
Hence, radius of the circle is 5 cm.