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  &#x2220A0B at centre and  &#x2220ACB at the circumference of the circle .
RT.P. : the angle in a semicircle is a right angle. ie : &#x2220 ACB= 90o

1   &#x2220AOB = 2&#x2220ACB  ||  angle at the centre is twice the angle at the circumference  of a circle.
2 . &#x2220ACB = ½&#x2220AOB  ||  by statement 1
3 . &#x2220ACB =½ x 180o  || As  &#x2220 AOB = 180o
4. &there4 &#x2220ACB = 90o  Proved

See also  Theorem | the angle subtended by an arc of a circle | at the centre is double the angle subtended by it at | any point on the remaining part of the circle