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.
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.
Prove that, given any three parallel lines, an equilateral triangle
always exists with one vertex on each of the three lines.
This problem is taken from the UKMT Mathematical Challenges.