| 翻訳と辞書 |
| bicentric quadrilateral ： ウィキペディア英語版 |
bicentric quadrilateral
In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and center of these circles are called the ''inradius'' and ''circumradius'', and ''incenter'' and ''circumcenter'' respectively. From the definition it follows that bicentric quadrilaterals have all the properties of both tangential quadrilaterals and cyclic quadrilaterals. Other names for these quadrilaterals are chord-tangent quadrilateral〔Dörrie, Heinrich, ''100 Great Problems of Elementary Mathematics: Their History and Solutions'', New York: Dover, 1965, pp. 188–193.〕 and inscribed and circumscribed quadrilateral. It has also been called a double circle quadrilateral.〔
If two circles, one within the other, are the incircle and the circumcircle of a bicentric quadrilateral, then every point on the circumcircle is the vertex of a bicentric quadrilateral having the same incircle and circumcircle.〔Weisstein, Eric W. "Poncelet Transverse." From ''MathWorld'' – A Wolfram Web Resource, ()〕 This was proved by the French mathematician Jean-Victor Poncelet (1788–1867).
==Special cases==
Examples of bicentric quadrilaterals are squares, right kites, and isosceles tangential trapezoids.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「bicentric quadrilateral」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|