问题 填空题
已知△ABC的外接圆的圆心O,BC>CA>AB,则
OA
OB
OA
OC
OB
OC
的大小关系为______.
答案

∵△ABC的外接圆的圆心O,BC>CA>AB,∠A>∠B>∠C,设△ABC的外接圆的半径为R,

∴cosA<cosB<cosC,

OA
OB
=OA×OB×cos2C=R2cos2C,

OA
OC
=R2cos2B,
OB
OC
=R2cos2A,由上知,cos2A<cos2B<cosC,

故答案为  

OA
OB
OA
OC
OB
OC

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