prove that angle in semi circle is 90 with prrof and diagram

Asked by ayush kumar | 3rd Mar, 2011, 01:39: AM

Expert Answer:

Dear student,
 
Let PQ be the diameter of the circle with centre O.
We have to prove that angle PRQ is 90o.
 
It is known that the angle subtended by an arc of a circle at its centre is twice the angle subtended by it at any point on the remaining part of the circle.

=> angle POQ = 2 angle PRQ

=> 180o = 2 angle PRQ [ angle POQ is 180o since POQ is a straight line] 

=> angle PRQ = 180o / 2 = 90o

We hope that clarifies your query.
 
Regards
Team
TopperLearning

Answered by  | 2nd Mar, 2011, 09:52: PM

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