tag:blogger.com,1999:blog-6933544261975483399.post1815417100068984772..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Problem 464: Square, Center, Arc, Angle, 120 DegreesAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-63475604511864561362019-01-16T12:03:49.196-08:002019-01-16T12:03:49.196-08:00Connect DE and observe that DEC is an equilateral ...Connect DE and observe that DEC is an equilateral triangle<br />Connect AE and BE and observe that AED congruent with BEC (SAS) => AE=BE <br />=> BED is congruent to AEC (SSS)<br />=> m(ECA)=m(BDE)<br />=> m(GCO)=m(GDO)<br />=> G,O,D,C are conyclic and since m(GCD)=60 => m(GOD)=120Sailendra Thttps://www.blogger.com/profile/12056621729673423024noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-44494887065517986032019-01-14T05:44:34.579-08:002019-01-14T05:44:34.579-08:00Tr.s AFD & CDE are equilateral
So < FDC = 3...Tr.s AFD & CDE are equilateral<br />So < FDC = 30<br /><br />Tr.s BFD & BED are congruent<br />So < ODF = 15 = < GCO<br />Hence ODCG is concyclic<br /><br />So < GOC = < GDC = 30<br />Implies < GOD = 120<br /><br />Sumith Peiris<br />Moratuwa<br />Sri LankaSumith Peirishttps://www.blogger.com/profile/06211995240466447227noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-62558633441524997442010-06-02T01:40:28.613-07:002010-06-02T01:40:28.613-07:00DOC=90deg, DGC=90deg ---> DCG+GOD=180deg.
DCG=6...DOC=90deg, DGC=90deg ---> DCG+GOD=180deg.<br />DCG=60deg ---> DOG=120degAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-74207201615438948102010-06-01T00:31:34.567-07:002010-06-01T00:31:34.567-07:00DEC =60° ( DEC equilateral )
in EGD, DEG = 60°...DEC =60° ( DEC equilateral )<br />in EGD, DEG = 60°, EDG = 30° ( ADG = 60° - 45°)<br />=> EGD = 90°<br />in EGD, EO, DO bisector ( O center, ODE = 60 - 45° )<br />=> GO bisector<br />=> OGD = 45°<br />=> DOG = 180° - ( 45° + 15°)<br /><br />=> DOG = 120°c .t . e. onoreply@blogger.com