1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
5 - Quadrilaterals
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

 

Tangents

Objective:

             • Learning about the basics of tangents

           • introductory to circumscribed and inscribed polygons and circles

 

Lesson 9-1 Tangents, Arcs, and chords:

               Circle: The set of points in a plane at a given distance from a given point in that plane

                Center: The given point of the circle

                Radius: The given distance of the circle

                Chord: A segment whose end points lie on a circle

             Secant: A line that contains a cord

             Diameter: A chord that contains the center of a circle

             Tangent: A line in the plane of a circle that intersects the circle in exactly one point

             Point of Tangency: The one point where the line intersects the circle. 

The tangent line l intersects the circle at point B. 

              Sphere: The set of all points in space that are a given distance from a given point.

Segment OA, OB,and OD are radii

Segment BD is a diameter

Segment BC is a chord

Line BC is a secant

Line t is a tangent

Point A the point of tangency

              Congruent circle: Circles or spheres that have congruent radii

            Concentric circles: Circles that lie in the same plane and have the same center. The rings of the target illustrate concentric circles.

 

           

             Concentric spheres: Spheres  that have the same center

             A polygon is inscribed in a circle and the circle is circumscribed about the polygon when each vertex of the polygon lies on the circle.

Theorem 9-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency Radius OT is perpendicular to the tangent line TZ   Corollary Tangents to a circle from a point are congruent. Segment MA is congruent to segment MB   Theorem 9-2 If a line in the  plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle. I is perpendicular to radius OB at B

When each side of a polygon is tangent to a circle, the polygon is Circumscribed about the circle and the circle is inscribed in the polygon

                Common Tangent: A line that is tangent to each of two coplanar cicles

             Common Internal Tangent : Tangent that intersects the segment joining the centers

                Common External Tangent: Tangent that does not intersect the segment joining the centers.

               Tangent circles: Coplanar circles that are tangent to the same line at the same point

      

     Circle A and Circle B are externally tangent.  

   Circle A and Circle B are internally tangent.  

 

 

Quickie Math Copyright (c) 2000 Team C006354