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.
This is another tough nut mind bender, and we have to give a
proof of existence. The conjecture is that, given any set of three
parallel lines, there always exists an equilateral triangle with
one of its vertices on each of the lines. The trouble with this
sort of mathematics is that there are infinitely many possible
cases. It means nothing that the conjecture holds true in every
case we test because it might still break down in a case we have
not tried. So what can be done? Playing with the dynamic diagram
suggests that the length of BC changes - how does it change?