Tangents
A tangent 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.
\(CT=5cm\) and \(PT=12cm.\)
What is the length of CP?
PT is a tangent and CT is a radius, therefore \(\angle CTP=90^\circ\).
(This right angle is not usually marked for you on the diagram. You have to deduce it is there because PT is a tangent to the circle.)
We have a right-angled triangle and so we can use Pythagoras:
\(C{P^2}={12^2}+{5^2}=169\)
\(CP=\sqrt{169}=13cm\)
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Calculating the volume of a standard solid
- Applying Pythagoras Theorem
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates
