Question:
Bisecting equally of an angle created by two intersecting chords of a circle if gone through the point of their intersection,
then prove that chords are equal.
Answer:
Let two chords AB and AC of a circle C(O, r) such that AB and AC are equally inclined to diameter AOD.
Now, draw OL perpendicular to AB and OM perpendicular to AC
In Δ OLA and Δ OMA,
∠OLA = ∠OMA {since each 90 degree}
∠OAL = ∠OAM {given}
OA = OA {common side}
So, Δ OLA ≅ Δ OMA
BY AAS Criterian,
OL = OM
=> chords AB and AC are equidistant from center O.
So, AB = AC
Hence, two chords are equal.
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