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If two chords of a circle are equally...

If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.

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Given Two chords AB and AC of a circle C(O,r) and AOD is a diameter such that `/_ AOB = /_ OAC`.
To Prove AB`=` AC
Construction Draw OL `_|_ AB` and `OM _|_ AC`.
Proof In `Delta OLA` and `Delta OMA` , we have
`/_ OLA =/_OAC` [each equal to `90^(@)]`
`OA =OA` [common]
`/_OAL=/_OAM` [given ]
`:. Delta OLA = ~= Delta OMA`
`implies OL =OM`
`implies` chords AB and AC are equidistant from O.
`implies AB=AC`.
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