x=dg(d−g)+bd(b−d)+bg(g−b)2a(d−g)+2f(b−d)+2c(g−b)+a2(d−g)+c2(g−b)+f2(b−d)2a(d−g)+2c(g−b)+2f(b−d)x=\dfrac{dg\left(d-g\right)+bd\left(b-d\right)+bg\left(g-b\right)}{2a\left(d-g\right)+2f\left(b-d\right)+2c\left(g-b\right)}+\dfrac{a^{2}\left(d-g\right)+c^{2}\left(g-b\right)+f^{2}\left(b-d\right)}{2a\left(d-g\right)+2c\left(g-b\right)+2f\left(b-d\right)}x=2a(d−g)+2f(b−d)+2c(g−b)dg(d−g)+bd(b−d)+bg(g−b)+2a(d−g)+2c(g−b)+2f(b−d)a2(d−g)+c2(g−b)+f2(b−d)
y=c−ab−dx+a2+b2−c2−d22b−2dy=\dfrac{c-a}{b-d}x+\dfrac{a^{2}+b^{2}-c^{2}-d^{2}}{2b-2d}y=b−dc−ax+2b−2da2+b2−c2−d2
等价问题:给一个三角形,三个顶点分别为 (a,b),(c,d),(f,g)(a,b),(c,d),(f,g)(a,b),(c,d),(f,g),求外心坐标。