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In geometry, Euler's theorem states that the distance d between the circumcentre and incentre of a triangle can be expressed as or equivalently where R and r denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively). The theorem is named for Leonhard Euler, who published it in 1767. However, the same result was published earlier by William Chapple in 1746. From the theorem follows the Euler inequality: which holds with equality only in the equilateral case.

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• Euler's theorem in geometry
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• In geometry, Euler's theorem states that the distance d between the circumcentre and incentre of a triangle can be expressed as or equivalently where R and r denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively). The theorem is named for Leonhard Euler, who published it in 1767. However, the same result was published earlier by William Chapple in 1746. From the theorem follows the Euler inequality: which holds with equality only in the equilateral case.
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• In geometry, Euler's theorem states that the distance d between the circumcentre and incentre of a triangle can be expressed as or equivalently where R and r denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively). The theorem is named for Leonhard Euler, who published it in 1767. However, the same result was published earlier by William Chapple in 1746. From the theorem follows the Euler inequality: which holds with equality only in the equilateral case.
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• EulerTriangleFormula.html
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• Euler Triangle Formula
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