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