Tangent Lines A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The point where a circle and a tangent intersect is the point of tangency.

Theorem 12.1 If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.

Theorem 12.2 If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.

Theorem 12.3 If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.

Finding Angle Measures Segment ML and segment MN are tangent to circle O. What is the value of x? LMNO is a quadrilateral. The sum of the angles is 360. 90 + 117 + 90 + x = 360 297 + x = 360 x = 63 The measure of angle M is 63°.

Finding a Radius What is the radius of circle C?

Identifying a Tangent Is segment ML tangent to circle N at L? Explain.

Real world example

Assignment Page 490-491 #1,2,3,4,7,8,9,10,11