# Tangents

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

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?

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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