TinhchatsaudaycUatrvctamtamgiaeco nhieu Lmg dl,lng trong giai cac bal tap hlnh hQC. Tinhchat.Cho AABCcoHlatnrctam,0la tamdlti1ng tronnqoal tiep va M la trungdiemBC. The thl AH= 20M. Chung minh. Xet tntong hop AABCnhon(cac tntonghopkhacehLmg minhtuang tl/). Vaduong kinhBD ella(0), VIDAB= 90nanDA.l AB. MaCH .1ABnanDA IICH. Tuang tl,l DCII AH. Suyra t(( giaeDAHClahlnhblnhhanh. Dod6DC=AH. MaDC=20M (vlOMla duong trungbinh ella aDBC)nan AH= 20M (dpcm), Biliap dl,lng Bilitoan1.ChoAABCnhonnitiepduong trontamO.G9iM,N vaPlan luqt la trungdiem caccanhBC,CAvaAB.Chltngminhrangcac duong quaMsongsongvaiOA,quaN songsongvaiOBvaquaPsongsongvaiOC dongquy.._ Loigiai.G9iHlatruetamAABC;I vaElan luqt la trung diemellaHA vaHO. ViAH = 20M nan AI= IH = OM. Ma AH 110M(doeung vuong g6e vaiBC)nan cact(( giae AIMO vaIHMOlahinhblnhhanh. . MOT TINHCHAT VETAMTAM61Ac D';NG HAlGIANG (GVTHCSThl tran Xuym, HiJ Tinh) Suyra MI II AOvaE la trungdiemellaMI. T((e laE thuoc duongquaM songsong vaiOA. Tuangtl,l E cling thuoc cac duongquaI\J songsongvaiOBvaquaPsongsongvaiOC. Tlt d6suyra dpem. Bidtoan 2. ChoAABCnhone6 H la tnrctam. Chltngminhrang9diemg6mchanbaduong cao,trungdiemba canh va trungdiemcacdoan HA,HB,HC dongviano LOigiai.sadunqhinhvevaehltngminhella biJi teen1 ta co: 1 1ED =EM =EI = -MI = -OA. 2 2 Sadl,lng cacketquatuangtl,l vakethopvai OA = OB = OC tasuyra 9 diemdaehocling thuoc duong trontamE. Bili toan3.ChoAABCnhonnitiepduong trontam0cocacduongcaoANvaCK.Duong tronnqoaltiepaBKN catduongtron(0) taldiem th((haiM.G9iIlatrungdiemellaAC.Chltng minh1M.1 MB. LOigiai.G9iHlatnrc, tamellaAABC,Jla trungdiemBH. Ta thayJlatamduongtron tiepaBKN vaBHla duongkinhella(J). t .............................................................................................. VI IHJOlahlnhblnhhanhnanIH IIOJ. khac,VIM,B la giaoellahai duong tron(0), (J)nanOJ 1- MB. SuyraIH 1- MB. MaBHla duong kinh ella(J)nanHM1- MB. Tli d6suyra \, H, Mhangva1M1- MB. Bcii toan 4.Cho tCtgiae ABCDni tiepduong tron(0 ; R). GQiH1, H2,H3, H4 thCt nr la tnrctam ella cactamgiae ACD,BCD, ABDva ABC. ChUng minhrang: a)BH1,AH2,CH3vaDH4dongquy. b)BonH1, H2,H3, H4 dongviano H3 Or H. D Li:fi giai. a) Vi AH1= BH2 (= 20M) va AH1II BH2 (vlcling vuongg6evaiCD)nan tCtAH1H2B lahlnhblnhhanh, Suyra AH2 vaBH1 catnhautaitrungI ellamoi duong. ChUng minh tuangnr vai cac cap khac ta suyra BH1,AH2,CH3 vaDH4 dong quytal trung I ellamoi duong (dpem). Vi tCtgiaeDOH4011ahinh blnh hanh nan 01H4: = OD=R.: ChUng minh tuangnr ta c6: 01 H1 =01 H2 =01H3=R.: bOnH3, H4 cilngthuQc:H1, H2, dLtOngtrontam0 1 bankinhR (dpcm). Bid toan 5. Cho dLtOngtrontam 0ban kinh R: vaP c6dinhnarn ngoai dl.tOngtron.Va M'p: tuyen PAva cat tuyen PBC (A, B, C nam trEm(0)).: Changminhrangkhicat tuyenPBC thayd6ithi:trve tam H ella MBC chay trim mt dLtOng cO dinh. : M : Li:fi gild.GQiI lahlnh ehieuella0trenBC,K la trungellaAH.Lay0' doixUng vai0qua trungellaPA. Ta thay0' la cO djnh va tCtgiae AOPO' la hlnhblnhhanh, Suyra O'PII AO va O'P= AO. COng vi tlt giae AOIK lahlnhblnhhanhnan AO IIKI va AO= KI. SuyraO'PIIKIvaO'P=KI.Tli d6tlt giae O'PIK lahlnhblnhhanh,Suyra O'KIIPI. MaPI 1-AKnan O'K 1-AK. Suyracan tal0' O'H = O'A. Tli d6H thueduong troncOdjnhtam0' ban kfnh O'A (dpem). Bcii til Bcii 1. ChUng minh rang tnrc tam, tronq tam va tam duong tronnqoal tiepellamt tam giae cling .nam trenmt duong (duong Ole). Bcii 2.Choduong tron(0) vaba A,B, C thay 95i tren (0) sao eho tnrc tamH ella MBC la mtcodinhnamtrong(0).Timquytieh b) Lay0 1 doixUng vai0quaI. chancacduongcaoellaMBC. ..................................................................... " Timottout 00 ilieu bien THAIHOU (Gv.THCSQuang U:,c, Can Lt?c,HaTfnh) CoratnhieuphLlong phapgiaimt?t bettoenbatdlmg thLic (BDT),nhLlng chUng ta can tim mt?tphLlong phap giai 99nnhat.chUng ta can t