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Show that angle subtended by an arc at the centre is double the angle subtended by it ay any point on the remaining part of a circle

Asked by kaaviyavelusamy 25th January 2016, 6:38 PM
Answered by Expert
Answer:

Let space straight O space be space the space centre space of space the space circle space and space BAC space be space the space angle space subtended space by space tbe space arc space BC. Join space AO comma space OC comma space OB space and space BC.  In space increment AOB AO space equals space OB space radius space of space the space circle angle BAO space equals space angle ABO space equals space straight x angle AOB space equals space 180 degree minus 2 straight x  In space increment AOC AO space equals space OC space radius space of space the space circle angle ACO space equals space angle OAC space equals space straight y angle AOC space equals space 180 degree minus 2 straight y   Now comma angle AOB space plus angle AOC plus angle BOC space equals space 360 degree space 180 degree minus 2 straight x plus space 180 degree minus 2 straight y space plus angle BOC space equals space 360 degree angle BOC space equals 2 straight x space plus space 2 straight y angle BOC space equals 2 left parenthesis straight x space plus space straight y right parenthesis angle BOC space equals 2 open parentheses angle BAC close parentheses

 

Answered by Expert 25th January 2016, 6:51 PM
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