Question

Chords AB and CD off a circle with centre O, interest at a point E. If OE bisects angle AED, prove that chord AB=chord CD.

Answer 1

Draw $OM\perp AB$ and $ON\perp CD$.

In $△OEM$ and $△OEN$,

$\angle OME=\angle ONE={90}^o$

$\angle OEM=\angle OEN$

$OE=OE$

Therefore, by AAS congruence,

$△OEM\cong △OEN$

So, $OM=ON$ [By cpct]

Chords AB and CD are equidistant from the centre.

So, Chord AB = Chord CD