Tangents Solve problems involving circumscribed polygons. Use properties of tangents. Solve problems involving circumscribed polygons.

TANGENTS I radius A C B tangent to circle point of tangency AC is tangent to circle I because the line containing AC intersects the circle at exactly one point. This point is called the point of tangency.

Theorem If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. I radius A C B tangent to circle point of tangency

Example 1 Find Lengths ED is tangent to circle F at point E. Find x. 4 3 x

Theorem If a line is perpendicular to the radius of a circle at its endpoint on the circle, then it is tangent to the circle. I radius A C B tangent to circle point of tangency

Example 2 Identify Tangents Determine whether MN is tangent to circle L. L 3 O 2 M 4 N

Example 3 Identify Tangents Determine whether PQ is tangent to circle R. 4 R P S 5 4 Q

MORE THAN ONE TANGENT More than one line can be tangent to the same circle. A D B C

Theorem If two segments from the same exterior point are tangent to a circle, then they are congruent. A B C

Example 4 Solve a Problem Involving Tangents Find x A 6x + 5 C -2x + 37 Q R B

Example 5 Triangles Circumscribed About a Circle Find the perimeter of triangle ADC if EC = DE + AF. D 6 E F C A B 19