Rhombus

Let $R$ be the radius of the large circle and $r$ be the radius of the smaller circle.

By considering $AD$ , we get that $R-r = 10$ .
By considering $AB$ , we get that $AB^2 = \left( \frac{AC}{2} \right)^2 + \left( \frac{BD}{2} \right) ^2$ , or that $400 = R^2 + r^2$ .

Recall that the area of a rhombus is half the product of the diagonals, thus we are interested in the value of $\frac{Rr}{2}$ . Squaring the first equation and subtracting the second, we obtain that $2Rr = ( R^2 + r^2) - (R-r)^2 = 400 - 100 = 300$ . Thus, the area of the rhombus is $\frac{Rr}{2} = \frac{300}{4} = 75$ .