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# Challenge problems: radius & tangent

Solve two challenging problems that apply properties of tangents to find the radius of a circle with a tangent.

## Problem 1

A, C, with, \overleftrightarrow, on top is tangent to circle O at point C.
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 O is broken into two line segments, A B and B O. Segment A B is two units. Segment A C is four units.
What is the length of start overline, O, C, end overline?
units

## Problem 2

A, C, with, \overleftrightarrow, on top is tangent to circle O at point C.
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 O is broken into two line segments, A B and B O. Segment A B is eighteen units. Segment A C is thirty units.
What is the length of start overline, O, C, end overline?
units