Point ‘$O$’ is the centre of the ellipse with major axis $AB$ and minor axis $CD$. Point $F$ is one focus of the ellipse. If$OF=6$ and the diameter of the inscribed circle of triangle $OCF$ is 2, then the product $AB·CD$ is equal to

a² - e² = 36$\Rightarrow$a² - b² = 36

Using r = (s - a)tan A/2 $∆$OCF
1 = (s - a)tan 45r where a = CF
2 = 2(s - a)
or 2 = 2S - 2a = 2s - AB
or 2 = (OF + FC + CO) - AB
$\begin{array}{l}2=6+\frac{\mathrm{AB}}{2}+\frac{\mathrm{CD}}{\mathrm{c}}-\mathrm{AB}\\ \frac{\mathrm{AB}-\mathrm{CD}}{2}=4\Rightarrow 2(\mathrm{a}-\mathrm{b})\Rightarrow \mathrm{a}-\mathrm{b}=4......\left(2\right)\end{array}$
Form (1) & (2) a + b = 9 $\Rightarrow$2a = 13; 2b = 5
$\Rightarrow$(AB)(CD) = 65