The numbers $a$, $b$ and $c$ are strictly positive. Let the $ABC$ be a triangle and the mobile point $M$ inside the triangle so $$\frac{MA}{a}=\frac{MB}{b}=\frac{MC}{c}.$$ What is the geometric location of the point $M$?
I'm sorry, but all my attempts have not materialized.
I think they are intersect points of two Apollonian circles.
Because we have $\frac{BM}{AM}=\frac{b}{a}$ and $\frac{CM}{AM}=\frac{c}{a}$.