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

We know that, tangent to a circle is perpendicular to the radius through the point of contact. So, $\angle OTP = {90^ \circ }$. In right angle triangle OTP, we have
$O{P^2} = O{T^2} + P{T^2} \\ \Rightarrow {13^2} = O{T^2} + {12^2} \\ \Rightarrow O{T^2} = {13^2} - {12^2} \\ \Rightarrow O{T^2} = 169 - 144 \\ \Rightarrow O{T^2} = 25 \\ \Rightarrow OT = 5 \\$