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.
From the measurements and the clue given find the area of the
square that is not covered by the triangle and the circle. Give
your answer as a formula and then calculate the area correct to two
decimal places. (This problem was created by Syed from Foxford
School and Community College).