在给定三边的坐标平面中绘制三角形 [英] Drawing a triangle in a coordinate plane given its three sides

问题描述

将给出三角形的三边的长度，a，b和c，并且我需要找到顶点的坐标。中心（可能是外围中心）可以是原点或（x，y）。

任何人都能指向正确的方向？

解决方案

我读过brainjam的答案，检查他的答案是否真实，他是对的。
计算：
O（0; 0），A（a; 0）和B（x; y）是三角形的三个点。 C1是A周围的圆，r1 = c; C2是O周围的圆，r2 = b。

C1：（x - a）*（x - a）+ y * y = c * c

C2：x * x + y * y = b * b

< y = b * b-x * x

（x - a）*（x - a）+ b * b - x * x = c * c >

x * x - 2 * a * x + a * a + b * b - x * x - c * c = 0

$ b b

2 * a * x =（a * a + b * b-c * c）

x =（a * a + b * b - c *（a * a + b * b-c * c）/（2 * a * b）* c） a））*（（a * a + b * b-c * c）/（2 * a））

p = （（a * a + b * b-c * c）/（2 * a））*（（a * a + b * b-c * c）/（2 * a）））

The length of three sides of the triangle, a, b and c will be given, and I need to find the coordinates of the vertices. The center (probably the circumcenter) can either be the origin or (x,y).

Can anyone point me in the right direction?

解决方案

I've read brainjam's answer and checked whether his answer is true and he is right. Calculation: O(0;0), A(a;0) and B(x;y) are the three points of the triangle. C1 is the circle around A and r1 = c; C2 is the circle around O and r2 = b. B(X;Y) is the intersection of C1 and C2, which means that the point is on both of the circles.

C1: (x - a) * (x - a) + y * y = c * c

C2: x * x + y * y = b * b

y * y = b * b - x * x

(x - a) * (x - a) + b * b - x * x = c * c

x * x - 2 * a * x + a * a + b * b - x * x - c * c = 0

2 * a * x = (a * a + b * b - c * c)

x = (a * a + b * b - c * c) / (2 * a)

y * y = b * b - ((a * a + b * b - c * c) / (2 * a)) * ((a * a + b * b - c * c) / (2 * a))

y = +- sqrt(b * b - ((a * a + b * b - c * c) / (2 * a)) * ((a * a + b * b - c * c) / (2 * a)))

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