问题
填空题
△ABC的外接圆圆心为O，且3
|
答案
∵△ABC的外接圆圆心为O，且3
+4OA
+5OB
=OC
，0
∴|
| =|OA
| =|OB
|，OC
=-OC
(3 1 5
+4OA
)，OB
∴
•OC
=|OC
|2OC
=
(31 25
+4OA
)2OB
=
|9 25
|2+OA 24 25
•OA
+OB
|16 25
|2OB
=|
|2+OC 24 25
•OA
，OB
∴24 25
•OA
=0，∴∠AOB=90°．外接圆中，OA=OB，OB
∴O为AC中点，
∵∠B为90°，
∴∠C=45°．
故答案为：45°．
