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How to prove that angle subtended by the chord are equal to the chords?

Asked by Preeti 11th March 2017, 7:38 PM
Answered by Expert
Error converting from MathML to accessible text.
I have proved it this way.
begin mathsize 20px style Given space colon space AB space and space CD space are space the space chords space that space ubtend space equal space angles space at space the space centre
that space is comma space angle AOB equals angle DOC
To space prove colon space AB equals CD
Proof colon
In space increment AOB space and space increment DOC comma
OB equals OC space left parenthesis radii space of space the space same space circle right parenthesis
angle AOB equals equals angle DOC space space left parenthesis given right parenthesis
OA equals OD space space left parenthesis radii space of space the space same space circle right parenthesis
So comma space increment AOB approximately equal to space increment DOC space left parenthesis SAS space congruence space criterion right parenthesis
rightwards double arrow AB equals CD space space left parenthesis CPCT right parenthesis
Hence space proved.
end style
Now, since the framing of your question is weird. I should tell you that the theorem can also be
If the chords are equal of a circle, then the angle subtended by them are also equal.
In that case you can use the same figure and prove the triangles congruent by the SSS congruence criterion, and then prove the angles equal by cpct.
Answered by Expert 11th March 2017, 8:03 PM
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