Question 4
In a plane, let $ABC$ be a triangle. Determine the locus of points $M$ in the plane such that
$$MA\cdot MA'=MB\cdot MB'=MC\cdot MC',$$
where $A',B',C'$ are the perpendicular projections of $M$ onto the lines $BC,CA,AB$, respectively.
$$MA\cdot MA'=MB\cdot MB'=MC\cdot MC',$$
where $A',B',C'$ are the perpendicular projections of $M$ onto the lines $BC,CA,AB$, respectively.