Two congruent chords of a circle are equidistant from its centre.

**NOTE:** Two chords are said to be congruent if they are equal in lengths.

Consider the equation of the circle

Suppose that and be congruent chords with , , and as shown in the given diagram. Since the circle passes through the points and , so equation of circle becomes

Since be the midpoint of the chord , so

Since be the midpoint of the chord , so

Now we shall find distance between and , as follows

Similarly, we can show that

Since and are congruent chords, so

Using equation (2) and (3), we get the following result

Adding on both sides of the above equation, we have

Using equation (vi) and (vii) in equation (viii), we get

This shows that the congruent chords of a circle are equidistant from its centre.