There are two equal circles of radius $1$ placed inside the triangle $ABC$ with side $BC = 6$. The circles are tangent to each other, one is inscribed in angle $B$, the other one is inscribed in angle $C$. (a) Prove that the centroid $M$ of the triangle $ABC$ does not lie inside any of the given circles. (b) Prove that if $M$ lies on one of the circles, then the triangle $ABC$ is isosceles.