Mix

Chord properties-
1. A line from the centre of a circle to the midpoint of a chord meets the chords at right angles
2. A perpendicular drawn to a chord from the centre of the circle bisects the chord
3. Equal arcs of a circle subtend equal angles at the centre
4. The perpendicular bisector of a chord must pass through the centre of the circle
5. The centre of a circle is the perpendicular bisector of chords

Angle Properties-
1. The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc
2. Angles at the circumference subtend on the same arc and are equal
3. The angle in a semi circle is a right angle

Cyclic quadrilateral-
1. Opposite angles in a cyclic quadrilateral are supplementary
2. The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle

Tangent properties-
1. Tangents are perpendicular to the radius at the point of contact
2. Tangents to a circle from an exterior point are equal

Ratio theorems-
1. The product of intercepts of intersecting chords are equal
2. The square of a tangent is equal to the product of the intercepts of a secant drawn from an external point
3. Products of intercepting secants from an external point are equal

Angles in alternate segments-
1. An angle formed by a tangent to a circle with a chord drawn to the point of contact is equal to any angle in the alternate segment

Two circle properties-
1. Two circles touch if they have a common tangent at the point of contact
2. When circles touch, the line of centre passes through the point of contact