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# 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  Answer Verified
Hint: Use the information that tangent to a circle is perpendicular to the radius through the point of contact.

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 $O{P^2} = O{T^2} + P{T^2} \\ \Rightarrow {13^2} = O{T^2} + {12^2} \\ \Rightarrow O{T^2} = {13^2} - {12^2} \\ \Rightarrow O{T^2} = 169 - 144 \\ \Rightarrow O{T^2} = 25 \\ \Rightarrow OT = 5 \\$
Hence the radius of the circle is 5 cm.
Note: Using the correct theorem is the key to solve this problem. After that Pythagoras theorem will give the required result.
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Radius of a Circle  Perpendicular Distance Of A Point From A Plane  Circumference of a Circle  Tangent of a Circle  Equation of A Circle  Secant of a Circle  Sector of a Circle  Area of a Circle  Area of a Circle Formula  Area of a Sector of a Circle Formula  