As shown in the figure, in the angle ABC, the angle c = 90 degrees, D and E are the points on AB and AC respectively, and ad · AB = AE · AC, then ed Is it perpendicular to ab? Please explain why

As shown in the figure, in the angle ABC, the angle c = 90 degrees, D and E are the points on AB and AC respectively, and ad · AB = AE · AC, then ed Is it perpendicular to ab? Please explain why

The proof process is as follows:
∵AD•AB=AE•AC
∴ AD/AC =AE/AB
∵∠A=∠A
∴△CBA∽△DEA
∵∠C=90°
∴∠EAD=90°
∴ED⊥AB.