Proof
Take the same point as in IV.13 (intersection of two
angle-bisectors). Join to each vertex; by I.4 the resulting
triangles are congruent (equal sides, common bisected angles), so the
five distances from to the vertices are equal. Draw the circle
on with that radius (Definition I.15).
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Full neighborhood
Depends on (3)
- IV.13Proposition IV.13In a given pentagon, which is equilateral and equiangular, to inscribe a circle.
- I.4Proposition I.4If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight…
- I.15Definition I.15A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among…
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