Circle Geometry

《Circle Geometry》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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)AAÐBOA=ÐCOD(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、RÐOMB=ÐOMA(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、OARÐANO=ÐBMO=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、DCXDAÐAXD=ÐCXB(verticallyopp)CAÐXAD=ÐXCB(Anglestandingonthesamearc)AÐXDA=ÐXBC(Anglesumoftr

26、iangle)XCorrespondsidesAXCX=XDXBAX.XB=CX.XDBDhttp://www.geocities.com/fatmuscle/HSC/6MathsExtension1–CircleGeometryExternally!Thesquareofthelengthofthetangentfromanexternalpointisequaltotheproductoftheinterceptsofthesecantpassingthroughthispoint.2(AX)=BX.CXABXCExternallyProveD