CIRCLESCIRCLES

SECTION 10-1

JIM SMITH JCHS

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A CIRCLE ISA CIRCLE ISA SET OF POINTSA SET OF POINTSEQUIDISTANCEEQUIDISTANCEFROM A GIVENFROM A GIVENPOINT CALLED POINT CALLED THE CENTERTHE CENTER

DEFINITIONDEFINITION

PARTS OF A CIRCLEPARTS OF A CIRCLE

CENTERCENTER

AA

PARTS OF A CIRCLEPARTS OF A CIRCLE

RADIUSRADIUSRADIIRADII

DISTANCEDISTANCEFROM CENTER FROM CENTER TO CIRCLETO CIRCLE

PARTS OF A CIRCLEPARTS OF A CIRCLE

CHORDSCHORDS

ENDPOINTS AREENDPOINTS AREON THE CIRCLEON THE CIRCLE

PARTS OF A CIRCLEPARTS OF A CIRCLE

AA

DIAMETERDIAMETER

CHORD THATCHORD THATCONTAINS CONTAINS THE CENTERTHE CENTER

PARTS OF A CIRCLEPARTS OF A CIRCLE

AA

dd = 2r = 2r

rr = d / 2 = d / 2

DIAMETERS OF CIRCLES A, DIAMETERS OF CIRCLES A, B, and C ARE 14, 20, and 10B, and C ARE 14, 20, and 10

BBAA

XX YYCC

FIND XB FIND BYFIND XB FIND BY

BBAA XX YY CC

FIND XBFIND XBXB = AB- AXXB = AB- AXXB = 10 – 7XB = 10 – 7XB = 3XB = 3

FIND BYFIND BYBY = BC – CYBY = BC – CYBY = 10 – 5BY = 10 – 5BY = 5BY = 5

CIRCUMFERENCECIRCUMFERENCEC = 2 C = 2 ππ r or C = d r or C = d ππ

1) FIND C if r = 7FIND C if r = 7 C = 2 C = 2 ππ 7 7 C = 14 C = 14 ππ or 43.96 or 43.96

2)2) FIND C if d = 12FIND C if d = 12 C = 12 C = 12 ππ or 37.68 or 37.68

5

5

FIND THE CIRCUMFERENCEFIND THE CIRCUMFERENCE

EXACT ANSWEREXACT ANSWER

NEAREST TENTHNEAREST TENTH

5

5

45,45,90 TRIANGLE45,45,90 TRIANGLE d = 5d = 5√√22

EXACT ANSWEREXACT ANSWERC = C = 55√√22ππ

NEAREST TENTHNEAREST TENTHC = 22.2C = 22.2