Question

Prove that angle in a semicircle is a right angle.

Answer 1

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 = 900proof:- 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 1800bcoz POQ is a straight line] ===> angle PRQ = 1800/ 2===> angle PRQ = 900.
HENCE PROOVED.
GIVE ME UR VALUABLE THUMBS UP IF MY PROOF IS RIGHT.