two equal chords AB and CD of a circle with centre O .when produced ,meet at a point E .prove that BE = DE and AE= CE

Question

Detail of figure - A circle with centre O and draw two equal chords opposite to centre O with slightly inclined when produced both chords meet at point E outside the circle 

Answer 1

Using the relation of arc measure to inscribed angles,

demonstrate that ∠ABC ≅ ∠CDB,

Then Δ EBD is isosceles.

The same can be done for ΔEAC.

Then AB = CD