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Tangents Drawn from an External Point

Find the leng...

Question

Find the length of a tangent drawn to a circle with radius 5 cm, from a point 13 cm from the centre of the circle.

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Solution

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

We have to find TP. 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 length of TP is 12 cm.

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