A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

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Solution

Let us put the given data in the form of a diagram.

We have to find OT. From the properties of tangents we know that a tangent will always be at right angles to the radius of the circle at the point of contact. Therefore is a right angle and triangle OTP is a right triangle.

We can find the length of TP using Pythagoras theorem. We have,

Therefore, the radius of the circle is 24 cm.

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