## Napoleon Variation Problem

Construct equilateral triangles *BAD*, *BCE* and *CAF* on the sides of a Δ*ABC*, and reflect each of them respectively in sides *BD*, *BE* and *CA*. What do you notice about the triangle *GHI* formed by the centres of the reflected triangles *A'BD*, *C'BE* and *F'CA*?

**Drag points ***A*, *B* or *C* to dynamically change the figure.

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Napoleon Variation Problem

**Challenge**: Can you logically explain (prove) this result (which is a variation of Napoleon's Theorem)? If after spending some considerable time with it, and you're still stuck, go to Hint.

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Michael de Villiers, 25 June 2011.