# 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.

-

## 1 Answer

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.

-
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

1
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
– anegligibleperson Dec 16 '12 at 21:23
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9564018249511719, "perplexity_flag": "middle"}