Elementary Geometry for College Students (6th Edition)

We call the vertices: $(0,0); (0,2b); (0,2a)$ Since the midpoint is on one side, we find that it is already known to be $d= \sqrt{b^2 +a^2}$ away from each vertex touching the hypotenuse. We use the distance formula from the origin to find: $d_2 =\sqrt{a^2+b^2}$ The two distances are equal.