EnGeometry in Figures

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1、GeometryinFiguresArseniyAkopyanLicenseAgreement:Ifyoudon’tlikethisbook,pleasedeleteitfromyourcomputer.Intheothercaseyoushouldbuyitoncreatespace.comoramazon.com.ArseniyAkopyan.GeometryinFigures.ThisbookisacollectionoftheoremsandproblemsinclassicalEuclideangeometr

2、yformulatedinfigures.Itisintendedforadvancedhighschoolandundergraduatestudents,teachersandallwholikeclassicalgeometry.CoverartcreatedbyMariaZhilkina.cA.V.Akopyan,2011.Contents1Elementarytheorems...............................62Trianglecenters....................

3、.............93Trianglelines...................................154Elementsofatriangle..............................184.1Altitudesofatriangle...........................184.2Orthocenterofatriangle.........................214.3Anglebisectorsofatriangle.............

4、..........234.4Thesymmediananditsproperties....................274.5Inscribedcircles..............................294.6Inscribedandcircumscribedcirclesofatriangle.............384.7Circlestangenttothecircumcircleofatriangle.............394.8Circlesrelatedtoatrian

5、gle........................424.9Concurrentlinesofatriangle.......................504.10Righttriangles...............................554.11Theoremsaboutcertainangles......................554.12Otherproblemsandtheorems.......................575Quadrilaterals......

6、............................595.1Parallelograms...............................595.2Trapezoids.................................615.3Squares..................................625.4Circumscribedquadrilaterals.......................635.5Inscribedquadrilaterals.......

7、...................665.6Fourpointsonacircle...........................685.7Altitudesinquadrilaterals.........................716Circles......................................736.1Tangentcircles..............................736.2Monge’stheoremandrelatedconstructio

8、ns................756.3Commontangentsofthreecircles.....................796.4Butterflytheorem.............................816.5Powerofapointandrelatedquestions........