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Exploring Circles: Understanding Chords and Angles

Dive into the fascinating world of circles with our guide about chords and angles. This section expands on the critical concepts of circle geometry, including the relationships of chords, secant segments, and tangents. Learn how to utilize similar triangles to solve problems involving chord intersections and secant segments sharing endpoints. Practice with diagrams and extra exercises to reinforce your understanding of these geometric principles and discover the connections to other shapes you've studied.

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Exploring Circles: Understanding Chords and Angles

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  1. 7.8 What More Can I Learn About Circles? Pg. 26 Chords and Angles

  2. 7.8 – What More Can I Learn About Circles? Chords and Angles As you investigate more about the parts of a circle, look for connections you can make to other shapes and relationships you have studied so far.

  3. 7.40 – SIMILAR TRIANGLES

  4. Similar 8 4 6 x = 8 4 8x = 24 x 6 x = 3

  5. If two chords intersect in the ______________ of a circle, then the ___________ of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. inside product ab = cd

  6. 7.41 – EXTRA PRACTICE Use the relationships in the diagrams below to solve for the variable.

  7. 3x = 45 x = 15

  8. 4x = 48 x = 12

  9. 2x = 25 5 x = 12.5

  10. If two secant segments share the same endpoint ____________ a circle, then the ______________ of the lengths of one secant segment and its external segment equals the _____________ of the lengths of the other secant segment and its external segment. outside product product c(c + d) a(a + b) =

  11. If a secant segment and a tangent segment share an endpoint ____________ a circle, then the product of the lengths of the secant segment and its external segment equals the ___________ of the length of the tangent segment. outside square a(a + b) x2 =

  12. 7.42 – EXTRA PRACTICE Use the relationships in the diagrams below to solve for the variable.

  13. 3x= 5(15) 3x = 75 x = 25

  14. 5(x + 5) = 6(10) 5x + 25 = 60 5x = 35 x = 7

  15. x2= 2(18) x2 = 36 x = 6

  16. 312= 20(x+ 20) 961 = 20x + 400 561 = 20x 28.05 = x

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