Proof
Inscribe a regular pentagon in the given circle by IV.11. At each
vertex draw the tangent (III.16); the five tangents bound the
circumscribed pentagon. Each tangent is perpendicular to its radius
(III.18), and by I.4 the right triangles formed at adjacent vertices
are congruent, so the circumscribed pentagon has equal sides and
equal angles.
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Full neighborhood
Depends on (4)
- IV.11Proposition IV.11In a given circle to inscribe an equilateral and equiangular pentagon.
- I.4Proposition I.4If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight…
- III.16Proposition III.16The straight line drawn at right angles to the diameter of a circle from its extremity will fall outside the circle,…
- III.18Proposition III.18If a straight line touch a circle, and a straight line be joined from the centre to the point of contact, the straight…
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