I have the following question:
Let a, b, and c be nonnegative real numbers, and let A=(0,0), B=(a,b), and C=(c,0) be points in the coordinate plane, such that AB=AC. Let D be the midpoint of ¯BC, let E be the foot of the altitude from D to ¯AC, and let F be the midpoint of ¯DE.
(a) Express the coordinates of points E and F in terms of a, b, and c.
(b) Show that line segments ¯AF and ¯BE are perpendicular.
And I am stuck on #b. I am almost done, but not sure how to prove that a^2+b^2=c^2. (not to be mistaken for the points)