# Theorem : The Angle in a Semi-Circle is a Right Angle

Theorem: The angle in a semicircle is a right angle

Given : A circle with centre 0 with � at centre and � at the circumference of the circle .

RT.P. : the angle in a semicircle is a right angle. ie : ∠ ACB= 90^{o}

Statements:

1 𢈊OB = 2� || angle at the centre is twice the angle at the circumference of a circle.

2 . � = ½𢈊OB || by statement 1

3 . � =½ x 180^{o} || As ∠ AOB = 180^{o}

4. &there4 � = 90^{o} Proved