# Thread: locus question. perpeendiculars dropped to three sides.

1. ## locus question. perpeendiculars dropped to three sides.

Find the locus of the points P within a given triangle ABC such that the distances from P to the sides of the given triangle can themselves be the sides of a certain triangle.

2. ## Re: locus question. perpeendiculars dropped to three sides.

Originally Posted by abhishekkgp
Find the locus of the points P within a given triangle ABC such that the distances from P to the sides of the given triangle can themselves be the sides of a certain triangle.
Let $A',\, B',\, C'$ be the points where the angle bisectors at $A,\,B,\,C$ meet the opposite sides of the triangle. My guess is that the condition for P is that it must lie inside the triangle $A'B'C'$. I think (without having checked carefully) that I can prove this using coordinate geometry, but I don't see how to tackle it using euclidean methods.