A straight line drawn from the centre of a circle to bisect a chord which is not a diameter is at right angles to the chord
The perpendicular to a chord from the center bisects the chord
Equal chords are equidistant from the center
Chords equidistant from the center are equal
The tangent at any point of a circle and the radius through the point are perpendicular to each other
If two circles touch, the point of contact lies on the straight line joining their centers
From any point outside a circle tangents can be drawn and they are equal in length
If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection
If a line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments
The angle that an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circle
Angles in the same segment of a circle are equal
Angle in a semi-circle is a right angle
If two arcs subtend equal angles at the centre, they are equal
Conversely, if two arcs are equal, they subtend equal angles at the centre
If two chords are equal, they cut off equal arcs
Conversely, if two chords cut off equal arcs, then the two chords are equal
If two chords intersect internally or externally then the product of the lengths of the segments are equal
