Finding the side lengths of a rectangle given a circle passing through one of its vertices and touching two of its sides

Question

A circle touches a rectangle $ABCD$ of side lengths $2a$ and $2b$ at $M$ and $N$ on sides $AB$ and $AD$ respectively. It also passes through the point $C$. If the perpendicular distance of the line $MN$ from point $C$ is $6cm$, then the value of $ab$ is?

Seems like a relatively easy question, but has proven to be quite difficult for me to solve. If we take the special case of $a=b$, in which case the rectangle degenerates into a square, then the solution comes out to be $9$, but I could not find a solution of general values of $a$ and $b$. Please help.

Answer 1

Hints :

Take $ND=y$ and $MB=x$ and $AN=NM=r$ Find other things in terms of these

1. Apply pythagorus in $\triangle NDC$
2. Also in $\triangle OTC$ T is perpendiculat from $O$ to $CD$
3. Also in $\triangle MBC$
4. Or any triangle that seems good.
5. Analyse $\triangle NMC$ Note that $\angle NCM=45^\circ$