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circles

circles. 10.1 Tangents to Circles. Circle Radius Diameter Chord Secant Tangent. Write the following down. Tangent. Circle. Radius. Diameter. Chord. Secant. Based on the picture write your own definitions….

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circles

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  1. circles 10.1 Tangents to Circles

  2. Circle • Radius • Diameter • Chord • Secant • Tangent Write the following down

  3. Tangent Circle Radius Diameter Chord Secant Based on the picture write your own definitions…

  4. Talk to the person NEXT TO YOU about what you got for each of your definitions. • Change your definition based on your conversations. Share your thoughts…

  5. Circle – a set of all points in a plane that are equidistant from a given point Radius – distance from the center to a point on a circle. Diameter – the distance across a circle through the center.

  6. Chord – • a segment whose endpoints are on the circle. • Is the diameter a chord? • Yes, but it passes through the center of the circle.

  7. Secant – • a line that intersects a circle in two points. • Tangent – • a line that intersects a circle at exactly one point.

  8. Draw two congruent circles. • What property do they share? • Circles are congruent if they have the same radius. 2 2 Congruent?

  9. c AD CD d

  10. k Common Internal Tangent – Intersects the segment that joins the centers of the two circles. D C j m Common External Tangent – Does not intersect the segment that joins the centers of the two circles. A B Common Tangents n

  11. Are these lines tangent to the circle???

  12. What can you conclude about tangent lines and the radius at the same pt.?

  13. Tangent lines are perpendicular to the radius at the same point.

  14. 16 12 20 Is the segment tangent to the circle?

  15. 144 + 256 = 400 • It’s a right triangle! • So the segment is perpendicular. So the segment is tangent. 16 12 20 Pythagorean thm.

  16. 10 12 15.5 Is the segment tangent to the circle?

  17. 144 + 100 = 240.25 • not a right triangle • So it’s not perpendicular. 10 12 15.5 Pythagorean thm.

  18. B 16 ft r C A r 8 ft Find the radius, given that BC is tangent to the circle, and therefore perpendicular to the radius.

  19. When will the purple segment be equal to the corresponding black segment?

  20. Are they equal yet?

  21. A C B Draw! (If two segments from the same exterior point are tangent to a circle, then they are congruent. CA = CB

  22. 2x + 10 4x - 15 Find x

  23. 2x + 10 = 4x-15 • 25 = 2x • 12.5 = x 2x + 10 4x - 15 Find x

  24. Homework Pg. 599: 18-28, 36-41, 46-48

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