See excircle in All languages combined, or Wiktionary
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "ex",
"3": "circle"
},
"expansion": "ex- + circle",
"name": "prefix"
}
],
"etymology_text": "From 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": "Entries with translation boxes",
"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": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Japanese translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Korean translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Swedish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Vietnamese translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Welsh translations",
"parents": [],
"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": "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.",
"type": "quote"
},
{
"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.",
"type": "quote"
}
],
"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"
},
{
"code": "cy",
"lang": "Welsh",
"sense": "escribed circle",
"tags": [
"masculine"
],
"word": "allgylch"
}
]
}
],
"sounds": [
{
"audio": "LL-Q1860 (eng)-Flame, not lame-excircle.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/56/LL-Q1860_%28eng%29-Flame%2C_not_lame-excircle.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-excircle.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/56/LL-Q1860_%28eng%29-Flame%2C_not_lame-excircle.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-excircle.wav.ogg"
}
],
"word": "excircle"
}
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "ex",
"3": "circle"
},
"expansion": "ex- + circle",
"name": "prefix"
}
],
"etymology_text": "From 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",
"Entries with translation boxes",
"Japanese terms with redundant script codes",
"Korean terms with redundant script codes",
"Pages with 1 entry",
"Pages with entries",
"Quotation templates to be cleaned",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with Japanese translations",
"Terms with Korean translations",
"Terms with Portuguese translations",
"Terms with Swedish translations",
"Terms with Vietnamese translations",
"Terms with Welsh translations",
"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": "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.",
"type": "quote"
},
{
"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.",
"type": "quote"
}
],
"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"
]
}
],
"sounds": [
{
"audio": "LL-Q1860 (eng)-Flame, not lame-excircle.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/56/LL-Q1860_%28eng%29-Flame%2C_not_lame-excircle.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-excircle.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/5/56/LL-Q1860_%28eng%29-Flame%2C_not_lame-excircle.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-excircle.wav.ogg"
}
],
"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"
},
{
"code": "cy",
"lang": "Welsh",
"sense": "escribed circle",
"tags": [
"masculine"
],
"word": "allgylch"
}
],
"word": "excircle"
}
Download raw JSONL data for excircle meaning in English (4.3kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.