# Geometry/Chapter 21

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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)

- Geometry Main Page
- Motivation
- Introduction
- Geometry/Chapter 1 Definitions and Reasoning (Introduction)
- Geometry/Chapter 1/Lesson 1 Introduction
- Geometry/Chapter 1/Lesson 2 Reasoning
- Geometry/Chapter 1/Lesson 3 Undefined Terms
- Geometry/Chapter 1/Lesson 4 Axioms/Postulates
- Geometry/Chapter 1/Lesson 5 Theorems
- Geometry/Chapter 1/Vocabulary Vocabulary

- Geometry/Chapter 2 Proofs
- Geometry/Chapter 3 Logical Arguments
- Geometry/Chapter 4 Congruence and Similarity
- Geometry/Chapter 5 Triangle: Congruence and Similiarity
- Geometry/Chapter 6 Triangle: Inequality Theorem
- 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
- 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