Point '0' is the centre of the ellipse with major axis $AB$ & minor axis $CD$. Point F is one focus of the ellipse. If $OF=6$ & the diameter of the inscribed circle of triangle OCF is $2$, then find the product $(AB) (CD)$.
In this I know $ae=6$ .
But how to use the information of inscribed circle
Hint: In $\Delta OCF$, use the property that from a point, the tangents drawn to the circle are of equal length. This shiuld give you $OC=x+2$, $CF=x+4$ and $OF=6$. Rest is simple pythagoras theorem.
This should give your $b$ and you already have $ae$. Rest I guess you can solve.