When a triangle is formed inside a semicircle, two lines from either side of the diameter meet at a point on the circumference at a right angle.
The angle in a semicircle is a right angle of .
In the diagram PR is a diameter and .
What is the size of ?
since it is the angle in a semicircle.
The three angles in the triangle add up to , therefore:
In the diagram KL is a diameter of the circle and is 8 cm long.
LM = 3 cm.
Calculate the size of KM.
KL is a diameter so we have an angle in a semicircle therefore .
We have a right-angled triangle and so can use Pythagoras.
KM is not the hypotenuse so: