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Tangents Drawn from an External Point

If P T is a t...

Question

If PT is a tangent at T to a circle whose centre is O and OP = 17 cm, OT = 8 cm, Find the length of the tangent segment PT.

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Solution

Let us 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 15 cm.

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