Today I have an interesting geometric problem as following:
Let $\triangle ABC $ be an arbitrary triangle. Points $M$ and $N$ on the side $AB$ are such that $AM=BN=\dfrac{AB}{3}$. Points $P$ and $Q$ on the side $BC$ are such that $BP=CQ=\dfrac{BC}{3}$. Points $R$ and $S$ on the side $CA$ are such that $CR=AS=\dfrac{CA}{3}$. Construct equilateral triangles $IMN$, $JPQ$, and $KRS$ external to the triangle $ABC$. Prove that $\triangle IJK$ is an equilateral triangle.
I think here we can use rotation !
My first idea is to use the axe but I have problems in coordinates of points?
Can assist
I'm thankful
Thanks!!