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Triangle $ABC$ has equilateral triangles drawn on its edges.
Points $P$, $Q$ and $R$ are the centres of the equilateral
triangles. Experimentation with the interactive diagram leads to
the conjecture that $PQR$ is an equilateral triangle.
There are many ways to prove this
result. Here we have chosen two methods, one which uses only the
cosine rule and one which uses complex numbers to represent
vectors, and multiplication by complex numbers to rotate the
vectors by 60 degrees.
