Question

In the given figure, chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD.

Answer 1

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.