Theorem 3.7
-If a line is tangent to the circle, then it is perpendicular to the radius drawn to the point of tangency.
of the lengths of the segment.

Theorem 3.8
-If a line in the plane of the circle is perpendicular to the radius at its endpoint on the circle, then it is tangent to the circle.

 

Theorem 3.9
-If two tangents are drawn to a circle from the same exterior point, then the tangent, segments are congruent.

 

Theorem 3.10
-If two chords intersect, then the product of the lengths of the segment of one chord is equal to the product of the lengths of the other chord.

 

Theorem 3.11
-If two segments  are drawn to a circlefrom an external point, then the product of the length of an secant, segment and its external is equal to the product of the other secant segment and its external segment.

 

Theorem 3.12
-If a secant and a tangent segment are drawn to a circle from an external point, then the product of the lengths of the secant segment and its external segment is equal to the square of the length of the tangent segment