CONO-SUR 1994 Problem 6

Consider a $\triangle {ABC}$ , with $AC \perp BC$ . Consider a point $D$ on $AB$ such that $CD=k$ , and the radius of the inscribe circles on $\triangle {ADC}$ and $\triangle {CDB}$ are equals. Prove that the area of $\triangle {ABC}$ is equal to $k^2$ .