In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by or equivalently where and 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 1765. However, the same result was published earlier by William Chapple in 1746. From the theorem follows the Euler inequality:

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In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by

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From Wikipedia (CC BY-SA 4.0).