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Chapter 10: Circles

Chapter 10: Circles. 10.1: Tangents to Circles. Learning Outcomes. I will be able to identify segments and lines related to circles. Vocabulary. Circle: A circles is a set of points that are equidistant from a given point, called the center. Vocabulary.

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Chapter 10: Circles

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  1. Chapter 10: Circles 10.1: Tangents to Circles

  2. Learning Outcomes • I will be able to identify segments and lines related to circles.

  3. Vocabulary • Circle: A circles is a set of points that are equidistant from a given point, called the center.

  4. Vocabulary • Radius: This is the distance from the center of the circle to a point on the circle. • Two circles are considered congruent if they have the same radius.

  5. Vocabulary • Diameter: The diameter is the distance across the circle through the center. The diameter is twice the radius, or d = 2r.

  6. Vocabulary • Chord: A chord is a segment whose endpoints are points on a circle. • In this example PR and PS are chords.

  7. Vocabulary • Secant: A secant is a line that intersects a circle in two points.

  8. Vocabulary • Tangent: a tangent line is a line that intersects a circle at one point. Where the tangent line intersects a circle is called a point of tangency.

  9. Common Tangents • Common tangents are either external or internal. Internal External

  10. Practice

  11. Activity • Draw a circle. • Draw a line tangent to your circle. • Draw the radius to your point of tangency. Think-Pair-Share What do you notice about the tangent line and the radius?

  12. Properties of Tangent Lines

  13. Is Line EF tangent to the circle? • To determine this we use the Pythagorean Theorem to see if these three lengths form a right triangle. • 11²+60² = 61² • 121 + 3600 • 3721 = 3721 • Since these lengths form a right triangle, EF is tangent to the circle

  14. Find the Radius of the circle. r² + 16² = (r+8)² r² + 256 = r² + 16r + 64 -r² -r² 256 = 16r + 64 192 = 16r 12 = r The radius is 12.

  15. More Properties of circles

  16. Find the value of x x² + 2 = 11 - 2 -2 x² = 9 x = 3

  17. Exit Ticket Homework • Tell whether AB is tangent to the circle. • 18-28, 36-41, 46-48

  18. Chapter 10.2 Arcs and Chords

  19. Learning Outcomes • I will be able to use arc addition postulate to find missing arc measurements • I will be able to use properties involving congruent chord/arcs to find missing measurements.

  20. Minor and Major Arcs • A minor arc is an arc that is less than 180 degrees and is typically expressed with two letters. • A major arc is an arc that is greater than 180 degrees and is typically expressed with three letters.

  21. Arc Addition Postulate

  22. Practice

  23. Theorems

  24. Theorems

  25. Practice • 22. We can conclude that segment AB and segment CD are equidistant from F. • 23. We can conclude that segment AB is congruent to segment CB and that they are equidistant from F. • 24. We can conclude that segment AD is congruent to segment BD.

  26. Practice

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