Geometry/Chapter 21

A collection of theorems about chords of a circle can be summarized as under.

1. If a straight line drawn from the centre of a circle bisects a chord which does not pass through the centre, it cuts the chord at right angles. Conversely, if it cuts the chord at right angles, it bisects it. (Euclid III. 3)

2. One circle, and only one, can pass through any three points not in the same straight line.

3.If from a point within a circle more than two equal straight lines can be drawn to the circumference, that point is the centre of the circle. (Euclid III. 9)

4.Equal chords of a circle are equidistant from the centre. Conversely, chords which are equidistant from the centre are equal. (Euclid III. 14)

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• Geometry/Chapter 7 Parallel Lines, Quadrilaterals, and Circles
• Geometry/Chapter 8 Perimeters, Areas, Volumes
• Geometry/Chapter 9 Prisms, Pyramids, Spheres
• Geometry/Chapter 10 Polygons
• Geometry/Chapter 11 $\mathbb {R} ,\mathbb {R} ^{2},\mathbb {R} ^{3}$
• Geometry/Chapter 12 Angles: Interior and Exterior
• Geometry/Chapter 13 Angles: Complementary, Supplementary, Vertical
• Geometry/Chapter 14 Pythagorean Theorem: Proof
• Geometry/Chapter 15 Pythagorean Theorem: Distance and Triangles
• Geometry/Chapter 16 Constructions
• Geometry/Chapter 17 Coordinate Geometry
• Geometry/Chapter 18 Trigonometry
• Geometry/Chapter 19 Trigonometry: Solving Triangles
• Geometry/Chapter 20 Special Right Triangles
• Geometry/Chapter 21 Chords, Secants, Tangents, Inscribed Angles, Circumscribed Angles
• Geometry/Chapter 22 Rigid Motion
• Geometry/Appendix A Formulae
• Geometry/Appendix B Answers to problems
• Appendix C. Geometry/Postulates & Definitions
• Appendix D. Geometry/The SMSG Postulates for Euclidean Geometry