Question

From the diagram given below, if for two chords AB and CD, AB = CD, which of the following is true?

(a) OM < ON

(b) OM > ON

(c) OM = ON

(d) OM ≠ ON

This question was addressed to me in class test.

This interesting question is from Circles through Three Points in chapter Circles of Mathematics – Class 9

Answer 1

In the given question, two chords AB and CD are equal in length, i.e., $AB=CD$. The points $O$ and $N$ are the perpendiculars dropped from the center of the circle to the chords AB and CD, respectively.

For two equal chords in a circle, the perpendiculars from the center to these chords will be equal in length. This is a standard property of circles: the perpendicular distance from the center of the circle to any chord is the same for two equal chords.

Thus, if $AB=CD$, then the perpendicular distances from the center of the circle to these chords, $OM$ and $ON$, will be equal.

Therefore, the correct answer is:

(c) OM = ON