Proof
Converse of III.26. Equal arcs subtend equal chords (apply the
superposition argument in reverse), and equal chords in equal
circles give equal central angles (I.8: SSS on the radius-chord-
radius triangles). Inscribed angles inherit via III.20.
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Depends on (4)
- III.20Proposition III.20In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same…
- III.26Proposition III.26In equal circles equal angles stand on equal circumferences, whether they stand at the centres or at the circumferences.
- I.8Proposition I.8If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they…
- III.1Definition III.1Equal circles are those whose diameters are equal, or whose radii are equal.
Required by (dependents) (3)
- III.29Proposition III.29In equal circles equal circumferences are subtended by equal straight lines.
- IV.11Proposition IV.11In a given circle to inscribe an equilateral and equiangular pentagon.
- VI.33Proposition VI.33In equal circles angles have the same ratio as the circumferences on which they stand, whether they stand at the…
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