Find the area of region ABC below

Through the vertices A and C of a triangle rectangle ABC. two circles are drawn tangents to the legs which intercept at points $D$ and $F$, if : $BF = 4$ ; calculate the area of region ABC.(Answer:$8$)

Not being able to understand what the figure of the question would be like... Would anyone be able to show how it would look?


Solution 1:

It is given that $\angle ABC=90^\circ$. The only way that a circle can be tangent to both leg $AB$ and leg $BC$ is if those legs each lie on a tangent to the circle, as in the diagram.

enter image description here

Can you see how the conclusion as to the area of the triangle follows?