◯ 三角形外心计算器（外接圆圆心与半径）Circumcenter of a Triangle Calculator (Circumradius)
由平面三点坐标求外心（三边垂直平分线交点）和外接圆半径。共线时无外心。本地处理。From three planar points get the circumcenter (intersection of perpendicular bisectors) and circumradius. Collinear points have none. Processed locally.
使用说明与常见问题How-to & FAQ
「三角形外心计算器（外接圆圆心与半径）」是什么？What is the Circumcenter of a Triangle Calculator (Circumradius) tool?
由平面三点坐标求外心（三边垂直平分线交点）和外接圆半径。共线时无外心。本地处理。From three planar points get the circumcenter (intersection of perpendicular bisectors) and circumradius. Collinear points have none. Processed locally.
如何使用「三角形外心计算器（外接圆圆心与半径）」？How do I use the Circumcenter of a Triangle Calculator (Circumradius) tool?
在「三角形外心计算器（外接圆圆心与半径）」中，填写「A x」、「A y」、「B x」、「B y」、「C x」等参数，结果会随输入实时计算并显示在下方。In the Circumcenter of a Triangle Calculator (Circumradius): Fill in "A x", "A y", "B x", "B y", "C x"; results are recalculated instantly as you type.
钝角三角形的外心在哪？Where is the circumcenter of an obtuse triangle?
在三角形外部。直角三角形的外心在斜边中点。Outside the triangle. For a right triangle it is the midpoint of the hypotenuse.
和重心、内心有什么不同？How does it differ from centroid or incenter?
外心是外接圆圆心；重心是三条中线交点；内心是内切圆圆心。Circumcenter is the circumcircle centre; centroid is medians; incenter is the incircle centre.
能举个计算实例吗？Can you show a worked example?
例如在「三角形外心计算器（外接圆圆心与半径）」中填 A x = 0，A y = 0，B x = 4，B y = 0，C x = 0，C y = 3，结果区显示：外心 x：2；外心 y：1.5；外接圆半径：2.5For example, entering A x = 0, A y = 0, B x = 4, B y = 0, C x = 0, C y = 3 in the Circumcenter of a Triangle Calculator (Circumradius) gives: Circumcenter x: 2; Circumcenter y: 1.5; Circumradius: 2.5
哪些输入会被检查？Which inputs are validated?
「三角形外心计算器（外接圆圆心与半径）」会检查这些输入——「A x」：必须填写，须为数字；「A y」：必须填写，须为数字；「B x」：必须填写，须为数字；「B y」：必须填写，须为数字；「C x」：必须填写，须为数字；「C y」：必须填写，须为数字；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Circumcenter of a Triangle Calculator (Circumradius) checks its inputs — "A x": required, must be a number; "A y": required, must be a number; "B x": required, must be a number; "B y": required, must be a number; "C x": required, must be a number; "C y": required, must be a number; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「三角形外心计算器（外接圆圆心与半径）」的设置：「A x」默认 0；「A y」默认 0；「B x」默认 4；「B y」默认 0；「C x」默认 0；「C y」默认 3。每次生成结果都按当前设置处理。Settings in the Circumcenter of a Triangle Calculator (Circumradius) — "A x" default 0; "A y" default 0; "B x" default 4; "B y" default 0; "C x" default 0; "C y" default 3. The result always uses the current settings.
计算精度如何？How precise are the results?
「三角形外心计算器（外接圆圆心与半径）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Circumcenter of a Triangle Calculator (Circumradius) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「三角形外心计算器（外接圆圆心与半径）」免费吗？需要注册吗？Is the Circumcenter of a Triangle Calculator (Circumradius) free? Do I need an account?
「三角形外心计算器（外接圆圆心与半径）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Circumcenter of a Triangle Calculator (Circumradius) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.