Question

Two chords intersect at a point on a circle and the diameter through this point bisects the angle between the chords. Prove that the chords have the same length. [2 Marks]

Answer 1

$OA=OC$ [Radius of the same circle]
$OB=OB$ [Common side]
$\angle OBA=\angle OBC$ [Given]
$\Rightarrow △OAB=△OCB$ [1 Mark]
$\Rightarrow AB=CB$
$\therefore$ The chords have the same length. [1 Mark]