Question

angle of the semi circle is 90 degree prove that

Answer 1

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 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.