Question

Chords AB and CD of a circle with centre O, intersect at a point E. If OE bisects $\angle$AED, then chord AB = CD.

• A. True
• B. False

Answer 1

The correct option is A

True

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

In $△$ OEN and $△$ OEM

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

$\angle$ OEM = $\angle$ OEN (given in question)

$\Rightarrow$ $\angle$ MOE = $\angle$ NOE

OE = OE (common arm)

$\therefore △$OEN ≅ $△$ OEM by A.A.S

$\Rightarrow$ OM = ON (cpct)

$\Rightarrow$ The chords AB and CD are equidistant from the centre.

$\Rightarrow$ AB = CD (chords equidistant from centre are equal)