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Question
If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.
Solution
Let AB and AC be two chords and AOD be a diameter such that
∠ BAO = ∠ CAO
Draw OL ⊥ AB and OM ⊥ AC.
Now prove, Δ OLA = Δ OMA
Then OL = OM ⇒ AB = CD. .....(Chords which are equidistant from the centre are equal.)
Hence proved.
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