Section 10.5 Notes: Tangents Learning Targets Students will be able to use properties of tangents. Students will be able to solve problems involving circumscribed polygons.

Vocabulary! in exactly one point. The point where the tangent and the    Tangent  A line in the same plane as a circle that intersects the circle in exactly one point.    Point of Tangency   Common Tangent The point where the tangent and the circle intersect. A line, ray, or segment that is tangent to two circles in the same plane. In each figure below, in l is a common tangent of circles F and G.

Example 1: a) Using the figure to the right, draw the common tangents. If no common tangent exists, state no common tangent.

Example 1: b) Using the figure to the right, draw the common tangents. If no common tangent exists, state no common tangent.

Vocabulary!   Theorem 10.10  In a plane, a line is tangent to a circle if and only if it is perpendicular to a radius drawn to the point of tangency.

Example 2: a) KL is a radius of circle K. Determine whether LM is tangent to circle K. Justify your answer.

Example 2: b) XY is a radius of circle X. Determine whether YZ is tangent to circle X. Justify your answer.

Example 2: a) In the figure, WE is tangent to circle D at W. Find the value of x.

Example 2: b) In the figure, IK is tangent to circle J at K. Find the value of x.

You Try! Determine if line AB is tangent to the circle. a.

Vocabulary!   Theorem 10.11 If two segments from the same exterior point are tangent to a circle, then they are congruent.

Example 4: a) AC and BC are tangent to circle Z. Find the value of x.

Example 4: b) MN and MP are tangent to circle Q. Find the value of x.

Circumscribed Polygons Vocabulary!   Circumscribed Polygons A polygon is circumscribed about a circle if every side of the polygon is tangent to the circle.

Example 5: a) The round cookies are marketed in a triangular package to pique the consumer’s interest. If is circumscribed about circle T, find the perimeter of triangle QRS.

Example 5: b) A bouncy ball is marketed in a triangular package to pique the consumer’s interest. If triangle ABC is circumscribed about circle G, find the perimeter of triangle ABC.

Summary! Draw a circumscribed triangle Draw a inscribed triangle  

Summary! Determine whether each segment is tangent to the given circle. Justify your answer. 2. Solve for x given PW and WQ are tangents.