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.

Answer 1

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.