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Properties of Tangents

Properties of Tangents. Objectives: To define and use circle terminology To use properties of tangents to a circle. Tangent. A tangent is a line that intersects a circle at exactly one point. The point of intersection is called the point of tangency. Tangent. Example 2.

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Properties of Tangents

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  1. Properties of Tangents Objectives: • To define and use circle terminology • To use properties of tangents to a circle

  2. Tangent A tangent is a line that intersects a circle at exactly one point. • The point of intersection is called the point of tangency

  3. Tangent

  4. Example 2 Explain why the wheels on a train are closer to being tangent to the rails than a car tire to the road.

  5. Example 4 Draw two coplanar circles that intersect in a) two points, b) one point, c) no points and have the same center.

  6. Common Tangents A line, ray, or segment that is tangent to two coplanar circles is called a common tangent.

  7. Example 5 Tell how many common tangents the circles have and draw them all.

  8. Common Tangents, II Common tangents come in two flavors: Common Internal Tangent: Intersect the segment that joins the centers of the circles Common External Tangent: Does not intersect the segment that joins the centers of the circles

  9. Example 5, Revisited Determine whether the common tangents are internal or external.

  10. Tangent Line Theorem In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.

  11. Example 6 The center of a circle has coordinates (1, 2). The point (3, -1) lies on this circle. Find the slope of the tangent line at (3, -1).

  12. Example 7

  13. Example 8

  14. Example 9

  15. Example 10

  16. Congruent Tangents Theorem Tangent segments from a common external point are congruent.

  17. Example 11

  18. Challenge Problem A circle has a radius of 6 inches. Two radii form a central angle of 60°. Tangent lines are drawn to the endpoints of each of the radii. How far from the center do the two tangent lines intersect? Due at end of class.

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