Geometry related question

Question

Point K is a point inside a triangle XYZ. Let G, H, I be the orthogonal projections of the point K on the sides YZ, ZX, XY respectively. Let the orthogonal projections of the point X on the lines YK and ZK be M and N respectively. Prove that the lines MH, NI, YZ are concurrent.

Answer 1

An orthogonal is a line segment that is drawn from a vertex of a triangle to the side opposite of that vertex.  Also, the line segment is perpendicular to that opposite side.

 

Knowing that, draw your triangle with the orthogonals as described in the problem.  Then after you drawn your triangle, look for the point that MH, NI, and YZ have in common.  If those line segments meet at a common point, then those lines are concurrent.