GCD and Number Theory

Question

I need help with a proof that begins as follows:

"We are given that $(a-c)(a+c)=(d-b)(d+b)$. If $\gcd(a-c, d-b)=k$ and $\gcd(a+c, d+b)=k$, prove that $h$ and $k$ are relatively prime."

Thanks for your help!