SOLUTION: Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC.
a) Draw a triangle ABC and then sketch
Algebra ->
Triangles
-> SOLUTION: Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC.
a) Draw a triangle ABC and then sketch
Log On
Question 1053918: Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC.
a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if triangle ABC is not isosceles (or equilateral).
b) Show that, regardless of choice of triangle ABC, we always have AX = BY = CZ. Answer by ikleyn(52884) (Show Source):
Actually, this problem was posted to the forum approximately one year ago.
I solved it, and later presented it as the lesson.
It is a classic advanced geometry problem of a Math Circle level.
