1. Obj. 55 Lines and Circles The student is able to (I can): Identify chords, tangents, and secants Use properties of tangents to solve problems

2. secant tangent point of tangency A line that intersects a circle at two points A line in the same plane as a circle that intersects it at exactly one point. The point where the tangent and a circle intersect. A B m C chord secant tangent point of tangency 3. congruent circles Two circles are congruent if and only if their radii are congruent. A B C D A C if AB CD AB CD if A C 4. concentric circles tangent circles Coplanar circles with the same center Two coplanar circles that intersect at exactly one point. internally tangent externally tangent 5. common tangent A line that is tangent to two circles. common external tangent common internal tangent 6. Thm 11-1-1 Thm 11-1-2 If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. If a line is perpendicular to a radius at a point on the circle, then it is tangent to the circle. BELine t Line t tangent to B B E t 7. Thm 11-1-3 If two segments are tangent to a circle from the same external point, then the two segments are congruent. S A N D SD ND 8. Examples The segments in each figure are tangent. Find the value of each variable. 1. 2. 2a + 4 5a 32 6y2 18y 5a 32 = 2a + 4 3a = 36 a = 12 6y2 = 18y y y 6y = 18 y = 3