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Rules of Circle Geometry The circle is the most fascinating shape in mathematics. The circle is a locus of all the points that are the same distance from one point. There are twelve rules in circle geometry 1. Equal arc/chord subtend equal angles at the centre. Equal angles stand on an equal arc/chord. 2. Equal chords are equal distance from the centre. Chords that are equal distance from the centre are equal. 3. The line from the centre of a circle to the centre of a chord is perpendicular to the chord. A perpendicular line from the chord to the centre bisects the chord. 4. The angle at the centre is twice the angle standing on the same chord/arc. 5. Angles on the same arc are equal. 6. Angles on a semi-circle is 90° 7. Cyclic Quadrilaterals are quadrilaterals where all four corners lie on a circle. The opposite angles of cyclic quadrilaterals are supplementary. 8. x+y=180° The angle between the radius and a tangent is 90° 9. Tangents drawn from an external point are equal. 10. Two chords or secants (AB and CD) intersecting at X, then AX.BX = CX.DX 11. A secant and a tangent (ABX and CX) intersecting at X, then AX.BX=CX^2 12. The angle between a chord and a tangent is equal to the angle in the alternate segment.