An equilateral triangle with vertices in 3 parallel planes

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Question from prajay, a teacher:

How to construct an Equilateral Triangle whose vertices lie on three
parallel lines, if the distances of two lines are 'a' and 'b' units
from the middle line.What is the length of the side of the
Equilateral Triangle ?.

Prajay,

The way to solve such a problem is to work backwards. Draw an equilateral triangle with parallel lines through the vertices A, B, C labeled so that A is on the top line, B in the middle, and C at the bottom. Note what happens to the line through C when the diagram is rotated through 60 degrees (counterclockwise) about B.

Chris

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