由拿破仑三角形推广到任意三角形

From Napoleou Triaugle to any Triangle

在任意一个三角形的三条边上分别向外(内)作三个彼此相似的三角形,则这三个三角形的外心构成的三角形与向外(内)作的三个三角形相似.在此命题的证明过程中发现了九圆三线共于一点.

If three similar triangles are constructed on the three sides of any triangle, either all outward, or all inward, then a triangle formed by themselves circumcentres of the former constructed triangles is similar with these three triangles. During the course of this proof we have found that the nine circles and three lines pass through one point.