Question

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 1

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).