23. Find the geometric locus of points $M$, located inside a given triangle, such that the distances from $M$ to the sides of the given triangle are equal to the sides of some triangle.
23. For distances $x, y, z$ to be the sides of a triangle, it is necessary and sufficient that the inequalities $x<y+z$, $y<z+x$, $z<x+y$ are satisfied. However, the set of points for which, for example, $x=y+z$ is a segment with endpoints at the feet of the angle bisectors (at the feet of the angle bisectors, two distances are equal, and the third is zero, so the equality holds; and from the previous problem, it follows that this equality holds for all points on the segment). Answer: the desired geometric locus consists of points located inside the triangle with vertices at the feet of the angle bisectors.