# Dependency of locus sets on the initial construction 1

- Author:
- Zoltán Kovács

Given a triangle ABC and a free point D we consider the orthogonal projections E, F and G of D onto the sides of the triangle. For what positions of D are points E and F equidistant to G?
We obtain the answer by typing

`LocusEquation[h==i,D]`

where h and i are the (lengths of the) segments joining F, G and E, G respectively.The correct positions of D are shown with green. Also the segments h and i are shown with the same color.

What types of loci can be obtained for those points D for which h=i? By dragging A, B and C, try to find the answer.