tag:blogger.com,1999:blog-6933544261975483399.post7856852457645302635..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Geometry Problem 1399: Triangle, Circumcircle, Perpendiculars, Angles, Congruence, Cyclic QuadrilateralAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6933544261975483399.post-44304007607580772002018-11-12T03:29:09.845-08:002018-11-12T03:29:09.845-08:00Is EFGC=cyclic=>α=<DCE=<FGH=α'.Is EFGC=cyclic=>α=<DCE=<FGH=α'.<br />APOSTOLIS MANOLOUDIShttps://www.blogger.com/profile/15561495997090211148noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-18268535070990727392018-11-12T00:46:26.338-08:002018-11-12T00:46:26.338-08:00Unghiul FEG = unghiul FCG (laturi perpendiculare)....Unghiul FEG = unghiul FCG (laturi perpendiculare).<br />De aici FECG circumscriptibil <br />=> unghiul FGE = FCE (1).<br />Unghiul AHE = unghiul AGE =90 <br />=> AHEG circumscriptibil <br /> Unghiul HAE = unghiul HGE . (2)<br /> Dar unghiul BAD = unghiul BCD (3)<br />Din (2) si (3) => unghi BCD= unghi HGE.(4)<br />Din (1) si (4) => α= α^,<br />Florin Popa, Comanesti, Romania<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-47505407379685142482018-11-11T23:56:00.345-08:002018-11-11T23:56:00.345-08:00Ang BAD = HGF + FGE ( AHEG )
Ang BAD = BCE + ECD...Ang BAD = HGF + FGE ( AHEG )<br />Ang BAD = BCE + ECD ( BD )<br />Ang FGE = FCE ( FECG )<br /> => HGF = ECD c.t.e.onoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-68826367844593701452018-11-11T17:48:20.653-08:002018-11-11T17:48:20.653-08:00Solution 2
Since AGEH & ABDC are both concycl...Solution 2<br /><br />Since AGEH & ABDC are both concyclic<br />< HEG = < BDC<br /><br />So in Tr.s BDC & HEG,<br />< HEG = < BDC<br />< EHG = < DBC since each angle = < CAD<br />Hence < EGH = < DCB<br /><br />But < EGF = < ECF<br /><br />So alpha = alpha’<br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-16970952611534803872018-11-11T17:21:04.515-08:002018-11-11T17:21:04.515-08:00Since CEFG is concyclic,
< ECF = < EGF = x ...Since CEFG is concyclic, <br />< ECF = < EGF = x say<br /><br />Now since AGEC is concyclic, <br />< EGH = < EAH = < DCB <br /><br />But < EGH = alpha + x and<br />< DCB = alpha’ + x and so<br /><br />alpha = alpha’<br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.com