Proof
With centre at the external point describe a circle (Postulate 3)
cutting the given line; bisect the chord by I.10; the line from the
external point to the midpoint is perpendicular by I.8.
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Full neighborhood
Depends on (3)
Required by (dependents) (7)
- II.12Proposition II.12In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides…
- II.13Proposition II.13In acute-angled triangles the square on the side subtending the acute angle is less than the squares on the sides…
- III.14Proposition III.14In a circle equal straight lines are equally distant from the centre, and those which are equally distant from the…
- III.15Proposition III.15Of straight lines in a circle the diameter is greatest, and of the rest the nearer to the centre is always greater than…
- IV.4Proposition IV.4In a given triangle to inscribe a circle.
- IV.13Proposition IV.13In a given pentagon, which is equilateral and equiangular, to inscribe a circle.
- XI.11Proposition XI.11From a given elevated point to draw a straight line perpendicular to a given plane.
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