If the consecutive vertices $z_1, z_2, z_3, z_4$ of a quadrilateral lie on a circle, prove that
$${|z_1-z_3|}\times{|z_2-z_4|}={|z_1-z_2|}\times{|z_3-z_4|} +{|z_2-z_3|}\times{|z_1-z_4|}$$
This problem is given in L.V. Ahlfors text 'Complex Analysis: An introduction to the theory of analytic functions of one complex variable'
My Attempt: By theorem,"The cross ratio $(z_1,z_2,z_3,z_4)$ is real if and only if the four points lie on a circle or on a straight line."
Let $(z_1,z_2,z_3,z_4)=r$ where $r$ is any real, from which I find that $$(z_1-z_3)(z_2-z_4)=r(z_2-z_3)(z_1-z_4)$$ Also $(z_1,z_2,z_3,z_4)=s$ from which $$(z_1-z_3)(z_2-z_4)=s(z_1-z_2)(z_3-z_4) $$ But, now I do not know how to find the values of $r$ and $s.$ Please help.
Tips:
$$(z_1-z_3)(z_2-z_4)=(z_1-z_2)(z_3-z_4)+(z_2-z_3)(z_1-z_4)$$