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  ∠A0B at centre and  ∠ACB at the circumference of the circle .
RT.P. : the angle in a semicircle is a right angle. ie : ∠ ACB= 90^o
Statements:

1   ∠AOB = 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 180^o  || As  ∠ AOB = 180^o
4. &there4 ∠ACB = 90^o  Proved

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