Euclid Book 4

Proposition 2

Construction

Statement

Statement HTML

To inscribe inside a given circle a triangle similar to a given triangle.

Construction steps

Construction Steps HTML

  • Let the circle through the point A centered at O be the given circle and △DEF the given triangle.
  • Construct GH that is tangent to the circle at point A.
  • Find a point C on the circle such that ∠CAH = ∠DEF.
  • Find a point B on the circle such that ∠BAG = ∠DEF.
  • Join BC. △ABC has been inscribed in the given circle and similar to the given △DEF.
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    Original statement

    ϵἰς τὸν δοθέντα κύκλον τῷ δοθέντι τριγώνῳ ἰσογώνιον τρίγωνον ἐγγράψαι.

    English translation

    In a given circle to inscribe a triangle equiangular with a given triangle.

    Computable version

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