Tangents

A tangent meets a circle at one point and one point only.

Tangent and radius circle diagram

The angle between a tangent and a radius is a right angle of 90^\circ.

Question

In this diagram C is the centre of the circle and PT is a tangent to the circle.

CT = 5 cm and PT = 12 cm.

What is the length of CP?

Right-angle triangle over circle, 1 side equal to the radius of 5cm, 1 side of 12cm

PT is a tangent and CT is a radius, therefore \angle CTP = 90^\circ.

We have a right-angled triangle, so we can use Pythagoras:

C{P^2} = {12^2} + {5^2} = 169

CP = \sqrt {169}  = 13cm

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