题目内容
三角形ABC的外接圆圆心为O且半径为1，若3O
+4O
+5O
=
则O
•A
=（ ）
| A |
| B |
| C |
| 0 |
| C |
| B |
A．
| B．-
| C．
| D．-
|
∵3
+4
+5
=
∴3
+4
=-5
∴9
2+24
•
+16
2=25
2
∵A，B，C在圆上
∴OA=OB=OC=1
∴
•
=0
∴
•
=-
(3
+4
)• (
-
)
=-
(3
•
+4
2-3
2-4
•
)
=-
故选B．
| OA |
| OB |
| OC |
| 0 |
∴3
| OA |
| OB |
| OC |
∴9
| OA |
| OA |
| OB |
| OB |
| OC |
∵A，B，C在圆上
∴OA=OB=OC=1
∴
| OA |
| OB |
∴
| OC |
| AB |
| 1 |
| 5 |
| OA |
| OB |
| OB |
| OA |
=-
| 1 |
| 5 |
| OA |
| OB |
| OB |
| OA |
| OA |
| OB |
=-
| 1 |
| 5 |
故选B．
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