Consider a circle with diameter $AB$ and center $O$, and let $C$ and $D$ be two points on this circle. The line $CD$ meets the line $AB$ at a point $M$ satisfying $MB < MA$ and $MD < MC$. Let $K$ be the point of intersection (different from $O$) of the circumcircles of triangles $AOC$ and $DOB$. Show that $\angle MKO = 90^{\circ}$
Problem 2:
Find, with proof, all real number solutions to the following:\[
(a^2 + 1)(b^2 + 1) = (ab + 1)(a + b)\]
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