In the adjoining figure. If two equal chords AB and CD of a circle intersect each other at E. then prove that chords AC and DB are equal.

In the adjoining figure. If two equal chords AB and CD of a circle int

1.	In the adjoining figure. If two equal chords AB and CD of a circle intersect each other at E. then prove that chords AC and DB are equal.
Answer» We have, `rArr` `oversetfrown(AB)congoversetfrown(CD)` (if two chords of a circle are equal then their corresponding arcs are congruent) Subtracting `oversetfrown(CB)` from both sides,we get `oversetfrown(AB)-oversetfrown(CB)congoversetfrown(CD)-oversetfrown(CB)` `rArr oversetfrown(AC)congoversetfrown(DB)` `rArr AC=DB` (if two arcs are congruent then their corresponding chords are equal).

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In the adjoining figure. If two equal chords AB and CD of a circle intersect each other at E. then prove that chords AC and DB are equal.

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