Question

f) In the figure given below, chords AB and CD of a circle with centre O intersect
at E. If OE bisects angle AED, prove that AB = CD.​

Answer 1

Answer:

Let AB and CD be the chords of a given circle intersecting  each other at point E.

Draw perpendiculars OV and OU on these chords.

In ∆OVE and ∆OUE

∠OVE = ∠OUE (Each 90°)

OE = OE (common)

∠OEV = ∠OEU (OE bisects angle AED or angle VEU)

∴ ∆OVE ≅ ∆OUE (AAS rule)

∴ OV = OU (by CPCT)

But these are the perpendiculars to chords AB and CD.

∴ AB = CD (Chord at equal distances from the center are equal)