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Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1223.
Is arc AC=arcBD=arcEF. ThereforeCE//AF.APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORRYDALLOS PIRAEUS GREECE
BDFE is a concyclic trapezoid, hence< EBD = < FEB = < ECD = @ say ....(1)Similarly ABDC is a concyclic trapezoid, hence < ACD = < CDB = CEB = @ say ...(2)From (1) and (2) < CEF = < ACE But < ACE and < AFE are supplementaryHence < CEF and < AFE are supplementary implying that AF//CESumith PeirisMoratuwaSri Lanka
Another method........Since BDFE and ABDC are concyclic trapezoids AC = BD = EF So in concyclic ACEF, AC = EF and the result follows
arc AC = arc BD, arc EF = arc BD=> arc EF = arc AC