CIRCLES AND SEGMENTCIRCLES AND SEGMENTMEASUREMENTMEASUREMENT

Jim SmithJim SmithJCHSJCHS

Section 10-7Section 10-7

COPY THESE NOTES AND COPY THESE NOTES AND DRAW THE DIAGRAMS. DRAW THE DIAGRAMS. USE THESE AND THE USE THESE AND THE

PRACTICE PROBLEMS AT PRACTICE PROBLEMS AT THE END AS EXAMPLES THE END AS EXAMPLES

FOR THE CLASS FOR THE CLASS ASSIGNMENTASSIGNMENT

aa

bbcc

dd

THE PRODUCT OFTHE PRODUCT OFTHE THE PARTS PARTS OF ONEOF ONECHORD CHORD == THE PRODUCT THE PRODUCT OF THE OF THE PARTSPARTS OF OF THE OTHER CHORDTHE OTHER CHORD

ab = ab = cdcd

77

xx44

55 7x = 207x = 207x= 207x= 207 77 7X = 2.86X = 2.86

7x = 4(5)7x = 4(5)

..66

xx44

(6+x) (6-x) = 4∙4(6+x) (6-x) = 4∙436-x²=1636-x²=1636-x²-36 = 16-3636-x²-36 = 16-36-x²= -20-x²= -20-x²/-1 = -20/-1-x²/-1 = -20/-1x² = 20x² = 20√√x² = √20x² = √20X = 4.47X = 4.47

Radius = 6, so Radius = 6, so one part= 6+xone part= 6+x

FOILFOIL

and the other and the other part= 6-xpart= 6-x

The diameter isThe diameter isperpendicular to perpendicular to the chord, so it the chord, so it bisects the chordbisects the chord

Whole Whole

segmentsegment

Outside part

Outside part

The outside part of The outside part of segment AB x thesegment AB x thewhole segment AB =whole segment AB =the outside part of the outside part of segment CB x thesegment CB x the whole segment CB whole segment CB

AA

BB

CC

55

77

1515

xx

Outside x Whole = Outside x Outside x Whole = Outside x WholeWhole

5(5(x+5x+5) = ) = 7(7(15+715+7))

little+little = little+little = bigbig

5x+25 = 5x+25 = 7(22)7(22)5x+25 = 1545x+25 = 154 5x = 1295x = 129 X = 25.8X = 25.8

xx

44

99

Tangent (the Tangent (the outside is outside is also the also the whole)whole)

Outside x Whole = Outside x Outside x Whole = Outside x WholeWholex∙x = 4∙9x∙x = 4∙9

We know the whole We know the whole sosowe don’t need to we don’t need to add add the little parts the little parts

x² = 36x² = 36√√x² = √36x² = √36 X = 6X = 6

TRY THESETRY THESE

88

5577 XX

33

XX

55

1414

11 22

1) 7X = 8(5)1) 7X = 8(5)

7X = 407X = 40

X = 40/7X = 40/7

X = 5.71X = 5.71

2) 3(X+3) = 5(14)2) 3(X+3) = 5(14) 3X+9 = 703X+9 = 70 3X+9-9 = 70-93X+9-9 = 70-9 3X = 613X = 61 X = 61/3X = 61/3 X = 20.33X = 20.33