CIRCLES AND SEGMENT MEASUREMENT Section 10-7 Jim Smith JCHS

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

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

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

. Radius = 6, so one part= 6+x and the other part= 6-x The diameter is 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 The diameter is perpendicular to the chord, so it bisects the chord

Whole segment 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

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

x Tangent (the outside is also the whole) 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

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

Answers 1) 7X = 8(5) 7X = 40 X = 40/7 X = 5.71 2) 3(X+3) = 5(14)