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1、MathsExtension1–CircleGeometryCircleGeometryPropertiesofaCircleCircleTheorems:!Anglesandchords!Angles!Chords!Tangents!CyclicQuadrilateralshttp://www.geocities.com/fatmuscle/HSC/1MathsExtension1–CircleGeometryPropertiesofaCircleRadiusMajorSegmentDiameterChordMinorSegmentTangentConcyclicp
2、ointsformaCyclicQuadrilateralSectorArcTangentsExternallyandInternallyConcentriccircleshttp://www.geocities.com/fatmuscle/HSC/2MathsExtension1–CircleGeometryCircleTheorems!Equalarcssubtendequalangelsatthelcentreofthecircle.!Iftwoarcssubtendequalanglesatthecentreofthecircle,thenthearcsare
3、equal.qOl=rqql!Equalchordssubtendequalanglesatthecentreofthecircle.
4、
5、!Equalanglessubtendedatthecentreofthecirclecutoffequalchords.qOq
6、
7、SOB=OC(radiusofcircle)AADBOA=DCOD(vert.opp.Angles)
8、
9、BSOA=OD(radiusofcircle)DBOAoDCOD(SAS)AB=DC(correspondingsidesinoD's)qOqD
10、
11、Chttp://www.geocities.com
12、/fatmuscle/HSC/3MathsExtension1–CircleGeometry!Aperpendicularlinefromthecentreofacircletoachordbisectsthechord.!Alinefromthecentreofacirclethatbisectsachordisperpendiculartothechord.O
13、
14、RDOMB=DOMA(straightline)HOB=OA(radiusofcircle)SOM=MO(common)DAOMoDBOM(RHS)AM=BM(correspondingsidesino
15、D's)OA
16、M
17、Bhttp://www.geocities.com/fatmuscle/HSC/4MathsExtension1–CircleGeometry!Equalchordsareequidistantfromthecentreofthecircle.!Chordsthatareequidistantfromthecentreareequal.
18、
19、OARDANO=DBMO=90°(Alinefromthecentreofacirclethatbisectsachordisperpendiculartothechord)NHAO=BO(RadiusofCirc
20、le)SNO=MO(given)DANOoDBMO(RHS)
21、
22、MOBhttp://www.geocities.com/fatmuscle/HSC/5MathsExtension1–CircleGeometryInternally!TheproductsofinterceptsofintersectingAchordsareequalAX.XB=CX.XDCXBDAProveDAXD
23、
24、
25、DCXDADAXD=DCXB(verticallyopp)CADXAD=DXCB(Anglestandingonthesamearc)ADXDA=DXBC(Anglesumoftr
26、iangle)XCorrespondsidesAXCX=XDXBAX.XB=CX.XDBDhttp://www.geocities.com/fatmuscle/HSC/6MathsExtension1–CircleGeometryExternally!Thesquareofthelengthofthetangentfromanexternalpointisequaltotheproductoftheinterceptsofthesecantpassingthroughthispoint.2(AX)=BX.CXABXCExternallyProveD
