See excircle on Wiktionary
Download JSON data for excircle meaning in All languages combined (3.9kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "ex",
"3": "circle"
},
"expansion": "ex- + circle",
"name": "prefix"
}
],
"etymology_text": "ex- + circle",
"forms": [
{
"form": "excircles",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "excircle (plural excircles)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms prefixed with ex-",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Japanese terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Korean terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"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": "quotation"
},
{
"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": "quotation"
},
{
"ref": "2016, Evan Chen, Euclidean Geometry in Mathematical Olympiads, page 61",
"roman": "Incircles and excircles often have dual properties.",
"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;.",
"type": "quotation"
}
],
"glosses": [
"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."
],
"id": "en-excircle-en-noun-dZBY6Kaq",
"links": [
[
"geometry",
"geometry"
],
[
"escribe",
"escribe"
],
[
"circle",
"circle"
],
[
"polygon",
"polygon"
],
[
"triangle",
"triangle"
],
[
"quadrilateral",
"quadrilateral"
],
[
"tangent",
"tangent"
],
[
"line",
"line"
],
[
"side",
"side"
]
],
"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": [
{
"word": "excentre"
},
{
"word": "excenter"
},
{
"word": "incircle"
},
{
"word": "ex-tangential"
}
],
"topics": [
"geometry",
"mathematics",
"sciences"
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "escribed circle",
"word": "viereen piirretty ympyrä"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "escribed circle",
"word": "vierusympyrä"
},
{
"code": "fr",
"lang": "French",
"sense": "escribed circle",
"tags": [
"masculine"
],
"word": "cercle exinscrit"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "bōsetsuen",
"sense": "escribed circle",
"word": "傍接円"
},
{
"code": "ko",
"lang": "Korean",
"roman": "bangjeobwon",
"sense": "escribed circle",
"word": "방접원"
},
{
"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"
}
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "ex",
"3": "circle"
},
"expansion": "ex- + circle",
"name": "prefix"
}
],
"etymology_text": "ex- + circle",
"forms": [
{
"form": "excircles",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "excircle (plural excircles)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "excentre"
},
{
"word": "excenter"
},
{
"word": "incircle"
},
{
"word": "ex-tangential"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English nouns",
"English terms prefixed with ex-",
"English terms with quotations",
"Japanese terms with redundant script codes",
"Korean terms with redundant script codes",
"Quotation templates to be cleaned",
"en:Geometry"
],
"examples": [
{
"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": "quotation"
},
{
"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": "quotation"
},
{
"ref": "2016, Evan Chen, Euclidean Geometry in Mathematical Olympiads, page 61",
"roman": "Incircles and excircles often have dual properties.",
"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;.",
"type": "quotation"
}
],
"glosses": [
"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."
],
"links": [
[
"geometry",
"geometry"
],
[
"escribe",
"escribe"
],
[
"circle",
"circle"
],
[
"polygon",
"polygon"
],
[
"triangle",
"triangle"
],
[
"quadrilateral",
"quadrilateral"
],
[
"tangent",
"tangent"
],
[
"line",
"line"
],
[
"side",
"side"
]
],
"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."
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "escribed circle",
"word": "viereen piirretty ympyrä"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "escribed circle",
"word": "vierusympyrä"
},
{
"code": "fr",
"lang": "French",
"sense": "escribed circle",
"tags": [
"masculine"
],
"word": "cercle exinscrit"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "bōsetsuen",
"sense": "escribed circle",
"word": "傍接円"
},
{
"code": "ko",
"lang": "Korean",
"roman": "bangjeobwon",
"sense": "escribed circle",
"word": "방접원"
},
{
"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"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-10 from the enwiktionary dump dated 2024-05-02 using wiktextract (a644e18 and edd475d). 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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