Question 3
Let $ABC$ be a triangle. Construct an equilateral triangle externally on each of its three sides, and let $\Delta$ be the triangle whose vertices are the centers of these three equilateral triangles. Similarly construct equilateral triangles internally on the sides of $ABC$, and let $\Delta'$ be the triangle of their centers. Prove that the area of $ABC$ equals the difference between the areas of $\Delta$ and $\Delta'$.