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{"type":"standard","title":"Euler's theorem in geometry","displaytitle":"Euler's theorem in geometry","namespace":{"id":0,"text":""},"wikibase_item":"Q1423818","titles":{"canonical":"Euler's_theorem_in_geometry","normalized":"Euler's theorem in geometry","display":"Euler's theorem in geometry"},"pageid":3338987,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Euler_theorem2.svg/330px-Euler_theorem2.svg.png","width":320,"height":312},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Euler_theorem2.svg/388px-Euler_theorem2.svg.png","width":388,"height":378},"lang":"en","dir":"ltr","revision":"1186497585","tid":"d1dc976f-8a12-11ee-a325-7267cf8e0d10","timestamp":"2023-11-23T15:13:13Z","description":"On distance between centers of a triangle","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Euler's_theorem_in_geometry","revisions":"https://en.wikipedia.org/wiki/Euler's_theorem_in_geometry?action=history","edit":"https://en.wikipedia.org/wiki/Euler's_theorem_in_geometry?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Euler's_theorem_in_geometry"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Euler's_theorem_in_geometry","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Euler's_theorem_in_geometry","edit":"https://en.m.wikipedia.org/wiki/Euler's_theorem_in_geometry?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Euler's_theorem_in_geometry"}},"extract":"In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by\n\nor equivalently\n\nwhere and denote the circumradius and inradius 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.","extract_html":"

In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by\n $\text{[math]}$ \nor equivalently\n $\text{[math]}$ \nwhere $\text{[math]}$ and $\text{[math]}$ denote the circumradius and inradius 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.

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