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In the following figureenter image description here

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.

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  • $\begingroup$ Point B has nothing to do with the question. Actually I drew it on a tool and made this typo $\endgroup$
    – Kshitij Singh
    Commented Dec 25, 2019 at 19:42
  • $\begingroup$ $DG$ being equal to $5$ there are not intersection $F$ (according to the graphic the point $G$ must be close to the point $C$) $\endgroup$
    – Piquito
    Commented Dec 25, 2019 at 20:52

1 Answer 1

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

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