Mathematics
In the given figure, two chords AB and CD of a circle intersect at a point P.
If AB = CD, prove that: arc AD = arc CB.
Circles
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Answer
In a circle, if two chords are equal, then their corresponding arcs are also equal.
Given,
⇒ chord AB = chord CD
⇒ arc AB = arc CD
From figure,
⇒ Minor arc AB = Minor arc CD
⇒ Minor arc AB - Minor arc BD = Minor arc CD - Minor arc BD
⇒ Minor arc AD = Minor arc CB
⇒ arc AD = arc CB.
Hence, proved that arc AD = arc CB.
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