Several Proofs of Ceva's Theorem by Students

EduMath 25 (12/2007)Similarly,BP [ BSA] andPC [ ASC]CQ [ CSB] .QA [ BSA]AR BP CQ [ ASC ] [ BSA][ CSB]So, 1RB PC QA [ CSB][ ASC][ BSA].Six Different Proofs of Ceva’s Theorem by the StudentsProof 1. (by Monzon Abel, Chan Chi Fai, Chan Ka Lun, Chan Wing YanJoyce, Hui Chiu Kit, Hui Man Wa, Wendy Chow, Kan Ka Yin, Lam Ching Yan,Lam Hiu Yue, Leung Ka Hei, Lo Ching Hoi, Mok Tung Hoi, Ning Man Chit, SoTsz Chung, Tan Pak Chiu, Nicole Tin, Tsang Ting Ho, Wong Cheuk Kwan,Wong Ching, Wong See Wai, Yu Lik Hang and Anglea Wu)YAXRQSBPFigure 2CLet X and Y be points on BQ produced and CR producedrespectively such that XAY is a straight line parallel to BC (figure 2).As ΔARY ~ ΔBRC and ΔAQX ~ ΔCQB , we haveAR YA CQ BC and .RB BC QA AXAs ΔASX ~ ΔPSB and ΔASY ~ ΔPSC , we haveBP PS PCBP AX , and so .AX SA YAPC YAAR BP CQ YA AX BCHence 1RB PC QA BC YA AX.77