tag:blogger.com,1999:blog-6933544261975483399.post3376478242405526321..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Dynamic Geometry Problem 1464: Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of AreasAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6933544261975483399.post-72372159071244873092020-03-25T05:36:54.282-07:002020-03-25T05:36:54.282-07:00Thank u. Same here!Thank u. Same here!Sumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-50536363610508856342020-03-24T09:43:40.354-07:002020-03-24T09:43:40.354-07:00Thanks you are big favorite of me for your solutio...Thanks you are big favorite of me for your solutionsc.t.e.onoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-49227035817461294892020-03-23T14:18:07.845-07:002020-03-23T14:18:07.845-07:00P1465
AE=AH, BE=BF, CG=FC, DG=DH => AE+BE+CG+D...P1465<br />AE=AH, BE=BF, CG=FC, DG=DH => AE+BE+CG+DG=AH+BF+FC+DH => <br />(AE+BE+CG+DG).R =(AH+BF+FC+DH).R<br />S yellow = S greenc.t.e.onoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-80094250390763174042020-03-22T22:57:03.826-07:002020-03-22T22:57:03.826-07:00Good solution, much simpler than mineGood solution, much simpler than mineSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-58322843402127529222020-03-22T14:33:35.432-07:002020-03-22T14:33:35.432-07:00APE(=PEB+)+APH(=PHD+)+CPG(=GPD+)+CPF(=FPB+)
=> ...APE(=PEB+)+APH(=PHD+)+CPG(=GPD+)+CPF(=FPB+)<br />=> S yellow(=S green)c.t.e.onoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-82921147052041891952020-03-22T00:52:01.532-07:002020-03-22T00:52:01.532-07:00From the midpoint theorem,
EF//AC//GH and FG//BD//...From the midpoint theorem,<br />EF//AC//GH and FG//BD//EH so EFGH is a parallelogram and by Problem 1463, <br /><br />S(PEF) + S(PGH) = S(PFG) + S(PEH) ....(1)<br /><br />Now S(ABCD) = S(ABC) + S(ACD) = 4.S(BEF) + 4.S(DGH) ...(2)<br /><br />Similary S(ABCD) = S(ABD) + S(BCD) = 4.S(AEH) + 4.S(CFG) ....(3)<br /><br />From (2) & (3), S(BEF) + S(DGH) = S(CFG) + S(AEH) ...(4)<br /><br />Add (1) + (4)<br /><br />S2 + S4 = S3 + S1<br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.com