Chord

In a circle, chords of equal length are at equal perpendicular distances from the centre. A perpendicular drawn from the centre to each chord bisects that chord. Since the chords are equal and the radii are equal, the resulting right triangles are congruent; hence their distances from the centre are equal. Options B and C are incorrect because they imply unequal distances. Exam tip: The converse is also true: chords equidistant from the centre are equal.

A circle theorem states that chords at equal distances from the centre are equal in length. Hence, the two chords have the same length. Option B describes the rule for chords at different distances from the centre, not equal distances. Exam tip: Remember the converse too—equal chords are equidistant from the centre.