# Do you know how to solve a system of one quadratic and one linear equation?

Geometry Level 3

The hypotenuse of the right-angled triangle $$ABC$$ has length $$AB=c=35$$. The square $$CDEF$$, whose side length is $$d=12$$, is inscribed in the triangle as shown above (pictured red).

If $$AC=b$$ is the longer leg of the triangle, and $$BC=a$$ is the shorter leg, find the value of $$b-a$$.

Hint: $$\triangle ABC \sim \triangle EBF$$.

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