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.
From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
Prove that, given any three parallel lines, an equilateral
triangle always exists with one vertex on each of the three lines.
(In the problem 'Pareq Calc' the existence of the equilateral
triangle was assumed.)
If you have Java enabled, it may help to use the dynamic diagram
below which shows three parallel lines and the fixed point
A on one of the lines. The points
B and C are free to move along
the other two parallel lines in such a way that the lengths
AB and AC are always equal.
Click and drag the red points.