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Circle Segment Measurement: Explained and Illustrated

Learn how to calculate circle segment measurements with detailed examples and practice problems. Copy these notes and diagrams to use for class assignments. Understand chord properties, segment parts, and tangent concepts.

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Circle Segment Measurement: Explained and Illustrated

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  1. CIRCLES AND SEGMENT MEASUREMENT Section 10-7 Jim Smith JCHS

  2. COPY THESE NOTES AND DRAW THE DIAGRAMS. USE THESE AND THE PRACTICE PROBLEMS AT THE END AS EXAMPLES FOR THE CLASS ASSIGNMENT

  3. a d c b THE PRODUCT OF THE PARTS OF ONE CHORD = THE PRODUCT OF THE PARTS OF THE OTHER CHORD ab = cd

  4. 7 5 4 x 7x = 4(5) 7x = 20 7x= 20 7 7 X = 2.86

  5. Radius = 6, so one part= 6+x and the other part= 6-x The diameter is perpendicular to the chord, so it bisects the chord 6 . x FOIL 4 (6+x) (6-x) = 4∙4 36-x²=16 36-x²-36 = 16-36 -x²= -20 -x²/-1 = -20/-1 x² = 20 √x² = √20 X = 4.47

  6. Whole segment Outside part B A The outside part of segment AB x the whole segment AB = the outside part of segment CB x the whole segment CB C

  7. 5(x+5) = 7(15+7) little+little = big 5 x 7 Outside x Whole = Outside x Whole 15 5x+25 = 7(22) 5x+25 = 154 5x = 129 X = 25.8

  8. Tangent (the outside is also the whole) x 4 Outside x Whole = Outside x Whole x∙x = 4∙9 9 x² = 36 √x² = √36 X = 6 We know the whole so we don’t need to add the little parts

  9. TRY THESE 1 2 X 8 X 7 3 5 5 14

  10. Answers 1) 7X = 8(5) 7X = 40 X = 40/7 X = 5.71 2) 3(X+3) = 5(14) 3X+9 = 70 3X+9-9 = 70-9 3X = 61 X = 61/3 X = 20.33

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