Theorem: The angle in a semicircle is a right angle
Given : A circle with centre 0 with ∠A0B at centre and ∠ACB at the circumference of the circle .
RT.P. : the angle in a semicircle is a right angle. ie : ∠ ACB= 90o
= 2∠ACB || angle at the centre is twice the angle at the circumference of a circle.
2 . ∠ACB = ½∠AOB || by statement 1
3 . ∠ACB =½ x 180o || As ∠ AOB = 180o
4. &there4 ∠ACB = 90o Proved