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7.) What is the tangent to a circle conjecture?

A tangent line of a circle is any line that intersects the circle in ONLY one point. These lines "just touch" the circle without traveling inside. A line that intersects a circle through two points is a secant line. Chords of circles lie on secant lines.

The precise statement of this conjecture is:

Tangent Conjecture I: Any tangent line to a circle is perpendicular to the radius drawn to the point of tangency. (top picture)

The pictures and information were found at the following site:

http://www.geom.uiuc.edu/~dwiggins/conj42.html