Euclid Book 4

Proposition 4

Construction

Statement

Statement HTML

To inscribe a circle in a given triangle.

Construction steps

Construction Steps HTML

  • Let △ABC be the given triangle.
  • Bisect ∠CAB and ∠CBA. These two angle bisectors intersect at O.
  • From O, draw a line that is perpendicular to AB and name the intersection D.
  • Construct the circle through the point D centered at O. the circle through the point D centered at O has been inscribed in the given △ABC.
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    Original statement

    ϵἰς τὸ δοθὲν τρίγωνον κύκλον ἐγγράψαι.

    English translation

    In a given triangle to inscribe a circle.

    Computable version

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