Question

how to prove that angle formed in a semicircle is 90°

Answer 1

Step-by-step explanation:

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

to proof :- angle PRQ is a right angle ie; angle PRQ = 900

proof:- 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 [NCERT THEOREM 10.8]

===> angle POQ = 2 angle PRQ.

===> 1800 = 2 angle PRQ [ angle POQ is 1800 bcoz POQ is a straight line]

===> angle PRQ = 1800 / 2

===> angle PRQ = 900.

HENCE PROOVED.

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