The tangent theorem states that if two segments are tangent to a circle and intersect one another, the length from where the segments touch the circle to where they intersect will be the same.

A

C

B

The radius of a circle is perpendicular to a line segment that is tangent to a circle at the point where the radius and the line segment intersect.

Line tangent to the circle

Radius

Radius is perpendicular to the tangent line at the point of tangency

Using this information you can solve for the unknown length of a line segment or the length of the radius if you known the length of the other line segment or radius.

A

C

B

O

A

C

B

O

A

C

B

O

A

C

B

O

Substitute in values and simplify.