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 $\overline{BC},$ let $E$ be the foot of the altitude from $D$ to $\overline{AC},$ and let $F$ be the midpoint of $\overline{DE}.$

(a) Express the coordinates of points $E$ and $F$ in terms of $a,$ $b,$ and $c.$

(b) Show that line segments $\overline{AF}$ and $\overline{BE}$ 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)

Pangolin14 Nov 26, 2020