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Geometry

Geometry. 9.2 Tangents. Tangent Definition. A line in the plane of a circle that intersects the circle in exactly one point. tangent. Theorem. If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. ●.

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Geometry

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  1. Geometry 9.2 Tangents

  2. Tangent Definition A line in the plane of a circle that intersects the circle in exactly onepoint. tangent

  3. Theorem If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. ●

  4. Converse of the previousTheorem 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. ●

  5. Corollary Tangents to a circle from a point are congruent. ● ●

  6. A D O C B Exercises 1. If OC = 15 and OB = 9, then BC = 12 3-4-5 Triple 15 9 2. If OC = 3√6 and BC = 6, then OB = 3√2 3√6 x²+ 6² = (3√6)² x x²+ 36 = 54 6 x² = 18 x = √18 = 3√2

  7. A D O C B Exercises 6. If m<COB = 60 and CB = 6√3, then AB = 12 30-60-90 Rt. ∆ 60˚ 6√3 7. If m<BCD = 70, then m<CBD = m<____ = CDB 55 Iso. ∆ 70˚

  8. A D O C B Answers to Exercises • 10 • 6√2 • 8 • 8. 25

  9. Common Tangents A line that is tangent to each of two coplanar circles. common tangent ● ● common tangent

  10. Internal vs. External Tangents A common external tangent does not. common external tangent ● ● A common internal tangent intersects the segment joining the centers of the circle. common internal tangent

  11. Tangent Circles Two coplanar circles that are tangent to the same line at the same point. There are two types: internally tangent circles externally tangent circles

  12. Circumscribed Polygons A polygon is circumscribed about a circle if each of its sides is tangent to the circle. A circle is inscribed in a polygon if each of the sides of the polygon is tangent to the circle.

  13. Exercises • Tell whether the circles are externally tangent, internally tangent, or not tangent. • Tell whether the line is a common external tangent, a common internal tangent, or neither. 9. 10. 11. • not tangent • com. ext. tangent a. int. tangent b. com. ext. tangent a. not tangent b. neither

  14. Exercises • Tell whether the circles are externally tangent, internally tangent, or not tangent. • Tell whether the line is a common external tangent, a common internal tangent, or neither. 12. 13. 14. • ext tangent • com. int. tangent a. not tangent b. com. int. tangent a. not tangent b. com ext. tangent

  15. 24 23 S R 1 3 2 C A B Q P 15 17 Exercises 15. Find AC P S 13 9 24 23 R 9 13 T Q 15 17 AC = 8 SP = 39 RQ = 40 PT = 22 QS = 22

  16. Homework pg. 335 WE #1-6, 8-10, 14-18 Bring Compass

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