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