if the angles subtended by the chords of a circle at the centre are equal,then the chords are equal
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PeehuChouksey:
the second last line is CD=AB . pls don't confuse nd take it as CO , as it's CD.
Answered by
35
let AB andCD be the chords of a circle with centre 0
where angle AOB is equal to angle COD
To prove:AB equal toCD
Proof: in triangle AOB and triangleCOD,we have
OA equal to OC (radii of a circle)
angle AOB equal to angleCOD
OB equal to OD(radii of a circle)
therefore triangle AOB congruent to triangleCOD(by SAS rule)
therefore AB equal toCD (by cpct)
where angle AOB is equal to angle COD
To prove:AB equal toCD
Proof: in triangle AOB and triangleCOD,we have
OA equal to OC (radii of a circle)
angle AOB equal to angleCOD
OB equal to OD(radii of a circle)
therefore triangle AOB congruent to triangleCOD(by SAS rule)
therefore AB equal toCD (by cpct)
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