Gradient QR =
PQRS is a square
(since ) (1)
Now also satisfies , using (d), and again using
Subtract this equation from (1):
or, if not, , by dividing through by the common factor.
Now . Hence for real values of . So .
Hence and so, eliminating in equation (1):
I seem to have proved this in the reverse order, so I suspect there may be another method. However, I think the above reasoning is quite sound!