△ABC的外接圆圆心为O,且3
|
∵△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°.