3. Equal chords, equidistant from centre. Equal chords of a circle are equidistant from the centre of the circle. In equal circles or in the same circle, equal chords are equidistant from the centre. Chords which are equidistant from the centre are equal.











Proof:
1. In the figure, triangle OAB is rotated through an angle AOA' to triangle OA'B' about O.

Since rotation preserves shape and size, AB = A'B' and OG = OH.













2. In the diagram, AB = CD
Then OM = ON. (equal chords, equidistant from centre)













Example:

In the diagram, O is the centre of the circle, AB = CD and OM = 10cm. Find the length of ON.













Solution:

AB = CD(given)
Therefore, ON = OM (equal chords, equidistant from centre)
= 10 cm