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.

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Presentation transcript:

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. 5. Write the definition of a circle and a sphere. What one phrase separates the two definitions? 6. Write the definition of a chord.

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?

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

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.

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

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.

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

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

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

Internal or External?

Find the values

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)