### Geometry of Circles

Basics of circles and related theorems: 1. Equal chords in equal circles are equidistant from the centres. 2. Chords in a circle that are equidistant from the centre are equal. 3. The perpendicular from the centre of a circle to a chord bisects the chord. 4. The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord. 5. Tangents to a circle from an external point are equal. 6. The angle at the centre of a circle is double the angle at the circumference standing on the same arc. 7. Angles in the same segment of a circle are equal. 8. The opposite angles of a cyclic quadrilateral are supplementary. 9. The angle of a semi-circle is a right angle. 10. The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.