# Proposition: 3.02: Chord Lies Inside its Circle

### (Proposition 2 from Book 3 of Euclid's “Elements”)

If two points are taken at random on the circumference of a circle then the straight line joining the points will fall inside the circle. * Let $ABC$ be a circle, and let two points $A$ and $B$ have been taken at random on its circumference. * I say that the straight line joining $A$ to $B$ will fall inside the circle. ### Modern Formulation

The circle is a convex figure. In particular, if any two points are chosen from the circumference of a circle, and a straight line is constructed on these points, then:

1. The segment between the endpoints on the circumference is a chord (i.e. its points are located inside the circle).
2. The segment between the endpoints on the circumference is a chord (i.e. its points are located inside the circle).

Proofs: 1

Corollaries: 1
Proofs: 2
Sections: 3

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### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014