In the figure below, circle, cm, cm, cm, and is a tangent, find the perimeter of the figure .
A tangent to a circle is perpendicular to the radius at its point of tangency.
is a tangent, so .
is the centre of the circle, and is the midpoint of chord .
We know that the straight line passing through the centre of a
circle and the midpoint of any chord is perpendicular to the
chord, so and triangle is right angled at .
Using Pythagoras' theorem,
Triangle is right angled at .
We have found the lengths of the unknown sides of the figure so we can calculate its perimeter: