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Question
In following figure .,XY and YZ are two equal chords of a circle with centre O. Prove that the bisector of ∠ XYZ passes through O.
Solution
Join OX and OZ
In Δ XOY and Δ ZOY
OX = YZ (radii of same circle)
XY = YZ (given)
OY = OY (common)
∴ Δ XOY ≅ Δ ZOY (SSS)
∴ ∠ OYX = ∠ OYZ (CPCT)
Hence , OY is the bisector of ∠XYZ passing through O.
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