This subsection is dedicated to the propositions of Book 3 of “Euclid’s Elements”.

| | | | created: 2014-11-13 22:31:53 | modified: 2014-11-13 22:32:00 | by: *bookofproofs*

## 1.**Proposition**: 3.01: Finding the Center of a given Circle

## 2.**Proposition**: 3.02: Chord Lies Inside its Circle

## 3.**Proposition**: 3.03: Conditions for Diameter to be a Perpendicular Bisector

## 4.**Proposition**: 3.04: Chords do not Bisect Each Other

## 5.**Proposition**: 3.05: Intersecting Circles have Different Centers

## 6.**Proposition**: 3.06: Touching Circles have Different Centers

## 7.**Proposition**: 3.07: Relative Lengths of Lines Inside Circle

## 8.**Proposition**: 3.08: Relative Lengths of Lines Outside Circle

## 9.**Proposition**: 3.09: Condition for Point to be Center of Circle

## 10.**Proposition**: 3.10: Two Circles have at most Two Points of Intersection

## 11.**Proposition**: 3.11: Line Joining Centers of Two Circles Touching Internally

## 12.**Proposition**: 3.12: Line Joining Centers of Two Circles Touching Externally

## 13.**Proposition**: 3.13: Circles Touch at One Point at Most

## 14.**Proposition**: 3.14: Equal Chords in Circle

## 15.**Proposition**: 3.15: Relative Lengths of Chords of Circles

## 16.**Proposition**: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle

## 17.**Proposition**: 3.17: Construction of Tangent from Point to Circle

## 18.**Proposition**: 3.18: Radius at Right Angle to Tangent

## 19.**Proposition**: 3.19: Right Angle to Tangent of Circle Goes Through Center

## 20.**Proposition**: 3.20: Inscribed Angle Theorem

## 21.**Proposition**: 3.21: Angles in Same Segment of Circle are Equal

## 22.**Proposition**: 3.22: Opposite Angles of Cyclic Quadrilateral

## 23.**Proposition**: 3.23: Segment on Given Base Unique

## 24.**Proposition**: 3.24: Similar Segments on Equal Bases are Equal

## 25.**Proposition**: 3.25: Construction of Circle from Segment

## 26.**Proposition**: 3.26: Equal Angles and Arcs in Equal Circles

## 27.**Proposition**: 3.27: Angles on Equal Arcs are Equal

## 28.**Proposition**: 3.28: Straight Lines Cut Off Equal Arcs in Equal Circles

## 29.**Proposition**: 3.29: Equal Arcs of Circles Subtended by Equal Straight Lines

## 30.**Proposition**: 3.30: Bisection of Arc

## 31.**Proposition**: 3.31: Relative Sizes of Angles in Segments

## 32.**Proposition**: 3.32: Angles made by Chord with Tangent

## 33.**Proposition**: 3.33: Construction of Segment on Given Line Admitting Given Angle

## 34.**Proposition**: 3.34: Construction of Segment on Given Circle Admitting Given Angle

## 35.**Proposition**: 3.35: Intersecting Chord Theorem

## 36.**Proposition**: 3.36: Tangent Secant Theorem

## 37.**Proposition**: 3.37: Converse of Tangent Secant Theorem