You may also like  problem icon  Three Way Split  Take any point
P inside an equilateral triangle. Draw PA, PB and PC from P
perpendicular to the sides of the triangle where A, B and C are
points on the sides. Prove that PA + PB + PC is a constant.
problem icon  Pareq Calc  Triangle ABC is an equilateral
triangle with three parallel lines going through the vertices.
Calculate the length of the sides of the triangle if the
perpendicular distances between the parallel lines are 1 unit
and 2 units.  problem icon  Pareq Exists  Prove that, given any
three parallel lines, an equilateral triangle always exists with
one vertex on each of the three lines.    This solution comes
from Soh Yong Sheng (Raffles Institution, Singapore).  First he
added a few lines and letters to the diagram:  Soh Yong SHeng's
solution.  Since the circles are tangent to the triangles, we
know that CE is perpendicular to GF, and AB is perpendicular to
GF. [A line touching a circle (tangent) is always perpendicular
to the radius which meets