1969 Canadian MO Problems/Problem 4
Let be an equilateral triangle, and be an arbitrary point within the triangle. Perpendiculars are drawn to the three sides of the triangle. Show that, no matter where is chosen, .
Let a side of the triangle be and let denote the area of Note that because Dividing both sides by , the sum of the perpendiculars from equals (It is independant of point ) Because the sum of the sides is , the ratio is always