Mathematics
If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.
Circles
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Answer
Let AB and AC be two chords.
AOD be a diameter such that ∠BAO = ∠CAO.
OL ⟂ AB and OM ⟂ AC.
In △OLA and △OMA,
OA = OA [common side]
∠OLA = ∠OMA = 90°
∠LAO = ∠MAO [AO bisects ∠A]
∴ △OLA ≅ △OMA [By A.A.S. rule]
Then,
OL = OM (By C.P.C.T.C.)
AB = AC [Chords which are equidistant from centre are equal]
Hence, proved that the two chords are equal.
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