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Tangents

Tangents. November 18 , 2009. Yesterday’s homework. 1. What is the difference between a secant and a tangent to a circle? 2. Write the definition of a radius of a circle. 3. Define congruent circles. 4. Define concentric circles.

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Tangents

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  1. Tangents November 18, 2009

  2. Yesterday’s homework 1. What is the difference between a secant and a tangent to a circle? 2. Write the definition of a radius of a circle. 3. Define congruent circles. 4. Define concentric circles. 5. Write the definition of a circle and a sphere. What one phrase separates the two definitions? 6. Write the definition of a chord.

  3. 8. Name two chords of the circle. 9. Describe AO in terms of circle O. 10. Name a tangent of the circle. 11. Describe HK in terms of circle O. 12. Describe FG in terms of circle O. 13. Describe AB in terms of circle O. 14. Name a sceant of the circle. 15. What is the length of AB? 16. What is the length of OB? 17. Name a diamter of the circle. 18. Name two radii of the circle. 19. What is the length of AO?

  4. Objectives • Learn the properties of tangents. • Apply the properties of tangents in writing.

  5. Properties of Tangents • Theorem: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

  6. More about properties of tangents • Corollary: Tangents to a circle from a point are congruent.

  7. Even more about properties of tangents • Theorem: 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.

  8. Inscribed and circumscribed, revisted • You can also inscribe a circle.

  9. Internal tangent • A common internal tangent intersects the segment joining the centers.

  10. External tangent • An external tangent does not intersect the segment joining the centers.

  11. Internal or External?

  12. Find the values

  13. Circumference • Circumference is the measurement of the distance around the edge of a circle. Also known as 'periphery' , 'perimeter'. • The formula is C= πd or C= π(2r)

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