问题 填空题
△ABC内接于以O为圆心的圆,且3
OA
+4
OB
-5
OC
=0.则∠C=______.
答案

3

OA
+4
OB
+5
OC
=
0

3

OA
+4
OB
=5
OC

9

OA
2+24
OA
OB
+16
OB
2
=25
OC
2

∵A,B,C在圆上

设OA=OB=OC=1

OA
OB
=0

根据3

OA
+4
OB
=5
OC
,得出A,B,C三点在圆心的同一侧,

∴∠C=135°

故答案为:135°.

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