See excircle in All languages combined, or Wiktionary
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"ref": "1979, Dan Pedoe, Circles: A Mathematical View, published 1995, page 10:",
"text": "Also since the circle of inversion cuts both excircles orthogonally, each excircle inverts into itself.",
"type": "quote"
},
{
"ref": "1999, Art Johnson, Famous Problems and Their Mathematicians, Teacher Ideas Press, page 174:",
"text": "Extend the sides of triangle QRS and construct the three excircles: One excircle is tangent to side QR and rays SQ and SR; one excircle is tangent to side SR and rays QS and QR; and one excircle is tangent to side SQ and rays RS and RQ.",
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{
"ref": "2016, Evan Chen, Euclidean Geometry in Mathematical Olympiads, page 61:",
"text": "Lemma 4.9 (The Diameter of the Incircle). Let ABC be a triangle whose incircle is tangent to #x5C;overline#x7B;BC#x7D; at D. If #x5C;overline#x7B;DE#x7D; is a diameter of the incircle and ray AE meets #x5C;overline#x7B;BC#x7D; at X, then BD#x3D;CX and X is the tangency point of the A-excircle to #x5C;overline#x7B;BC#x7D;.\nIncircles and excircles often have dual properties.",
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"An escribed circle; a circle outside a polygon (especially a triangle, but also sometimes a quadrilateral) that is tangent to each of the lines on which the sides of the polygon lie."
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"raw_glosses": [
"(geometry) An escribed circle; a circle outside a polygon (especially a triangle, but also sometimes a quadrilateral) that is tangent to each of the lines on which the sides of the polygon lie."
],
"related": [
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"word": "excentre"
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{
"word": "excenter"
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{
"word": "incircle"
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"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "escribed circle",
"word": "viereen piirretty ympyrä"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "escribed circle",
"word": "vierusympyrä"
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{
"code": "fr",
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"sense": "escribed circle",
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"word": "cercle exinscrit"
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"roman": "bōsetsuen",
"sense": "escribed circle",
"word": "傍接円"
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"sense": "escribed circle",
"word": "방접원"
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"sense": "escribed circle",
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"masculine"
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"word": "círculo exinscrito"
},
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"sense": "escribed circle",
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"common-gender"
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"word": "utvändig tangeringscirkel"
},
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"code": "vi",
"lang": "Vietnamese",
"sense": "escribed circle",
"word": "đường tròn bàng tiếp"
}
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"word": "excircle"
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{
"ref": "1999, Art Johnson, Famous Problems and Their Mathematicians, Teacher Ideas Press, page 174:",
"text": "Extend the sides of triangle QRS and construct the three excircles: One excircle is tangent to side QR and rays SQ and SR; one excircle is tangent to side SR and rays QS and QR; and one excircle is tangent to side SQ and rays RS and RQ.",
"type": "quote"
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"ref": "2016, Evan Chen, Euclidean Geometry in Mathematical Olympiads, page 61:",
"text": "Lemma 4.9 (The Diameter of the Incircle). Let ABC be a triangle whose incircle is tangent to #x5C;overline#x7B;BC#x7D; at D. If #x5C;overline#x7B;DE#x7D; is a diameter of the incircle and ray AE meets #x5C;overline#x7B;BC#x7D; at X, then BD#x3D;CX and X is the tangency point of the A-excircle to #x5C;overline#x7B;BC#x7D;.\nIncircles and excircles often have dual properties.",
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"(geometry) An escribed circle; a circle outside a polygon (especially a triangle, but also sometimes a quadrilateral) that is tangent to each of the lines on which the sides of the polygon lie."
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"code": "fi",
"lang": "Finnish",
"sense": "escribed circle",
"word": "viereen piirretty ympyrä"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "escribed circle",
"word": "vierusympyrä"
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"sense": "escribed circle",
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"word": "cercle exinscrit"
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"sense": "escribed circle",
"word": "傍接円"
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"sense": "escribed circle",
"word": "방접원"
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"code": "pt",
"lang": "Portuguese",
"sense": "escribed circle",
"tags": [
"masculine"
],
"word": "círculo exinscrito"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "escribed circle",
"tags": [
"common-gender"
],
"word": "utvändig tangeringscirkel"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "escribed circle",
"word": "đường tròn bàng tiếp"
}
],
"word": "excircle"
}
Download raw JSONL data for excircle meaning in English (3.8kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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