Prove that the angle in a semi-circle is a right angle.
proof of this theorem:-
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.
GIVE ME UR VALUABLE THUMBS UP IF MY PROOF IS RIGHT.