Question

Chords which are ___________ from the centre are equal.

(a) unequal

(b) equidistant

(c) one third

(d) two third

I had been asked this question in an internship interview.

Origin of the question is Loci of Points topic in portion Lettering Practice, Scales & Curves of Civil Engineering Drawing

Answer 1

Correct option is (b) equidistant

Explanation: In the figure below, for ∆’s AOM and CON

OM = ON                                          (to prove)

OA = OC                                           (radii of the same circle)

AM = CN OR 2AM = 2 CN             (since OM ON are perpendicular to the chords and it bisects the chord and AM = MB, CN = ND)              

Angle AMO and CNO = 90°

∆AOM similar to ∆CON                     (R.H.S rule)

 OM = ON (CPCT)                           (required).