Geometry/Chapter 21

A collection of theorems about chords of a circle can be summarized as under.

1.''' If a straight line drawn from the centre of a circle bisects a chord which does not pass through the centre, it cuts the chord at right angles. Conversely, if it cuts the chord at right angles, it bisects it.''' (Euclid III. 3)

2. One circle, and only one, can pass through any three points not in the same straight line.

3.If from a point within a circle more than two equal straight lines can be drawn to the circumference, that point is the centre of the circle. (Euclid III. 9)

4.'''Equal chords of a circle are equidistant from the centre. Conversely, chords which are equidistant from the centre are equal'''. (Euclid III. 14)