(2002•深圳)阅读材料,解答问题:
命题:如图,在锐角△ABC中,BC=a,CA=b,AB=c,△ABC的外接圆半径为R,则
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/0.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/1.png)
=
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=2R.
证明:连接CO并延长交⊙O于点D,连接DB,则∠D=∠A.
因为CD是⊙O的直径,所以∠DBC=90°,
在Rt△DBC中,sin∠D=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/3.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/4.png)
,
所以sinA=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/5.png)
,即
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/6.png)
=2R,
同理:
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/7.png)
=2R,
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/8.png)
=2R,
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/9.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/10.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/11.png)
=2R,
请阅读前面所给的命题和证明后,完成下面(1)(2)两题:
(1)前面阅读材料中省略了“
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/12.png)
=2R,
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/13.png)
=2R”的证明过程,请你把“
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/14.png)
=2R”的证明过程补写出来.
(2)直接运用阅读材料中命题的结论解题,已知锐角△ABC中,BC=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/15.png)
,CA=
![manfen5.com 满分网](http://img.manfen5.com/res/CZSX/web/STSource/20131021232557702612188/SYS201310212325577026121022_ST/16.png)
,∠A=60°,求△ABC的外接圆半径R及∠C.
考点分析:
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