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# Determining tangent lines: lengths

Solve two problems that apply properties of tangents to determine if a line is tangent to a circle.

## Problem 1

Segment start overline, O, C, end overline is a radius of circle O.
A circle centered around point O. Segment O C is a radius of the circle. Point A lies outside the circle, and line A C is a line that could potentially be tangent to circle O. A line segment connects point A to point O and intersects the circle at point B. Line segment A O, line segment O C, and line A C create the triangle A O C. Side A C of the triangle is eleven units. Side O C of the triangle is five units. Side A O is broken into two line segments, A B and B O. Line segment A B is eight units. Line segment B O is unknown.
Note: Figure not necessarily drawn to scale.
Is line A, C, with, \overleftrightarrow, on top tangent to circle O?