平面几何难题

IBM平面几何难题：https://www.research.ibm.com/haifa/ponderthis/challenges/August1998.html

We have a triangle ABC, with a point D on side AB, E, on side BC, and F on side CA. The smaller triangle, DEF, is equilateral. The line segments AD, BE, and CF all have equal length.
Problem: Prove that ABC is also equilateral.

如何证明这个看似结论显然却难以证明的平面几何命题？

 证明:存在无穷多个边长均为整数的直 角三角形 ,其中任意两个都不相似.