BC

Abstract. In this article we propose to determine the triangles ’ class i i iA B C orthohomological with a given triangle ABC, inscribed în the triangle ABC ( , , i i iA BC B AC C AB ∈ ∈ ∈). We’ll remind, here, the fact that if the triangle i i iA B C inscribed in ABC is orthohomologic with it, then the perpendiculars in, i iA B, respectively in iC on, BC CA, respectively AB are concurrent in a point iP (the orthological center of the given triangles), and the lines, , i i iAA BB CC are concurrent in point (the homological center of the given triangles). To find the triangles i i iA B C, it will be sufficient to solve the following problem. Problem. Let’s consider a point iP in the plane of the triangle ABC and i i iA B C its pedal triangle. Determine the locus of point iP such that the triangles ABC and i i iA B C to be homological. Solution. Let’s consider the triangle ABC, (1,0,0), (0,1,0), (0,0,1)A B C, and the point ( , ,), 0iP α β γ α β γ+ + =. The perpendicular vectors on the sides are