Finding the lengths of lines outside of a circle when they're not tangent

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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That would mean the answer is 20.71? That doesn't make a lot of sense in the whole grand scheme of things Given the the line it's attached to is similar in length. –  Nathan Abbott Dec 16 '12 at 21:08
He's got the formula wrong. Try $x(x+7)=5(5+29)$. –  Mario Carneiro Dec 16 '12 at 21:12
Well, the problem is that the drawing doesn't make much sense either, because the 29 shouls look aprox. like 6 times the 5 segment, and it doesn't. Try making the drawing with some geometry software to see if it's actually that 20.71, you can try GeoGebra, it's online and free. –  MyUserIsThis Dec 16 '12 at 21:13
Mario is right though. This is a direct result of the power of a point: en.wikipedia.org/wiki/Power_of_a_point –  anegligibleperson Dec 16 '12 at 21:23