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In the adjoining figure, two chords AB and CD of a circle intersect at P. If AB = CD, prove that arc AD = arc CB.

In the adjoining figure, two chords AB and CD of a circle intersect at P. If AB = CD, prove that arc AD = arc CB. Circle, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Circles

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Answer

Given AB = CD

Since, in a circle, equal chords cut off equal arcs.

∴ arc AB = arc CD

Subtracting arc BD from both sides we get,

⇒ arc AB - arc BD = arc CD - arc BD

⇒ arc AD = arc CB.

Hence, proved that arc AD = arc CB.

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