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http://imgur.com/QFu05

I recreated the question in paint above ^ The line is not tangent to the circle.

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They're geometrically powers, so it must be that 5·29=x·7, assuming 5 and x are the lengths from the intersection point to the point in which the lines first cut the circle (the short ones)

He's right, I made a mistake: from the formula, it must be what he says: x(x+7)=5(5+29). The answer is 10, again, it doesn't make sense with your drawing, but your drawing is not accurate with the lengths of the segments.

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    Mario is right though. This is a direct result of the power of a point: http://en.wikipedia.org/wiki/Power_of_a_point2012-12-16