Track / Stage 5 / 23 of 400 #623 of 1964

Problem 623

AIME late

Geometry Difficulty 5.1 Find the answer

Draw an equilateral triangle in such a way that its vertices lie on three given straight lines, which are in the same plane and equidistant from each other.

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

Official solution

We bring the three lines into a parallel position with some plane (for example, the second one), and by constructing the equilateral triangle (K. M. L. VII. 86. page) we restore it to its original plane.

(Tóbiás J. László.)

The problem was also solved by: Pintér Miksa.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.