Question 67
A line $d$ is said to *focus* a triangle $T$ if there exists a point in the plane whose projections on the sides of the triangle $T$ all lie on the line $d$. Triangles $T_1$ and $T_2$ are *equivalent* if the set of focusing lines of $T_1$ is identical to the set of focusing lines of $T_2$. For any given triangle $T$ in the plane, prove that there exists exactly one equilateral triangle equivalent to $T$.