Circles Theorems

equal chords of a circle subtend equal angles at the center

If angles subtended by the chords of a circle at the center are equal, then the chords are equal

the perpendicular from the center of a circle to a chord bisects it

The line drawn through the center of a circle to bisect a chord is perpendicular to the chord

Equal chords of a circle/ congruent circles are equidistant from the center(s)

1. take 3 points a,b,c 2) join ab and bc 3) draw perpendicular bisectors of AB and BC 4) Their point of intersection is O

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle

Angles in the same segment of a circle are equal.

If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle (i.e. they are concyclic).