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Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 706.
∠EBO =∠OBA-∠EBA =(90°-∠BCA)-(90°-∠BDA)=∠BDA-∠BCA=∠DBC=∠EFO (since EF⊥DB and OF⊥CB)∴ E,O,F,B are concyclic
Note that OE and OF are perpendicular bisectors of AB and AC.So angle(EOF) supplement to angle(EOF) and E,O,F,B are concyclic
Sorry Peter cannot understand
To SumithYou are right. " OE and OF are perpendicular bisectors of AB and AC." is not enough to conclude that E,O,F,B are cocyclic.addition work to show that angle(ABE)= angle(CBF) is required. Thanks Sumith
EO perpend AB, OF perp BC =>BE'E + BF'O = 180(E' on AB, F' on BC)