Question 806126
DE is perpendicular to AC
GF is perpendicular to AX

so DE is parallel to GF

In triangle DEC & GFC

angle DEC is congruent to triangle GFC
Angle EDC is congruent to FGC   ( corresponding angles)

so the triangles are similar by AA test of similarity

Therefore EC/FC = ED/FG = DC/GC  ratios of corresponding sides are equal

But EC = AC ( diagonals of a parallelogram bisect each other)


Therefore (AC+FC)/FC = (ED+FG)/FG    ( by componendo)