A geometry (circles and tangents) problem

Question

In the following figure

There is a circle with centre at origin. D and E are two tangent points of the circle from point C. FGHI is a rectangle and it is given that DG=5 and GI=4. And I have to find the length of EH

I tried solving this question could not solve it. Is the question correct? If it is please provide the solution.

Answer 1

Extend $HF$ to cut the circle second time at $J$. By the power of the point $H$ with respect to the circle we have $$HE^2 = HF\cdot HJ = HF\cdot (HF+2DG) =4\cdot 14 $$

so $$HE = 2\sqrt{14}$$