Question

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

Answer 1

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.