Question

prove that angles in a semicircle is 90 degree.

Answer 1

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Answer 2

Answer:

Given:- PQ is a dimeter of a circle C (O,r) and angle PRQ is an angle in a semi circle.

To prove:- angle PRQ is a right angle

[angle PRQ = 90°]

Proof:-  Since, The angle subtended by an arc of a circle at its centre is twice the angle formed by the same arc at a point on the circle .

=) angle POQ = 2 angle PRQ.

=)180° = 2 angle PRQ

[ angle POQ is 180° as  POQ is as straight line]

=)  angle PRQ = 180° / 2

=) angle PRQ = 90°

Hence, Proved

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