Tangents
A A straight line that just touches a point on a curve. A tangent to a circle is perpendicular to the radius which meets the 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 = 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:
\(C{P^2} = {12^2} + {5^2} = 169\)
\(CP = \sqrt {169} = 13cm\)
