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Question
In the given figure, chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD.
Solution
Chord AB ≅ Chord CD ...(Given)
∴ Arc ACB ≅ Arc CBD ...(Arcs corresponding to congruent chords.)
∴ m(arc ACB) = m(arc CBD) ...(1)
But m(arc ACB) = m(arc AC) + m(arc CB) ...(2)
and m(arc CBD) = m(arc CB) + m(arc BD) ...(3)
From (1), (2), and (3), we get,
m(arc AC) + m(arc CB) = m(arc CB) + m(arc BD)
∴ m(arc AC) = m(arc BD)
∴ arc AC ≅ arc BD
Hence, proved.
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