已知A（0,1/n）B（0,-2/n）C（4+1/n,0）其中n为整数,设Sn表示△ABC外接圆的面积,则limSn=?n趋向于无穷

Question

已知A（0,1/n）B（0,-2/n）C（4+1/n,0）其中n为整数,设Sn表示△ABC外接圆的面积,则limSn=?
n趋向于无穷

Answer 1

用三点发可得圆心
x=(16n^2+8n-3)/(4n^2+2n)
y=-1/(2n)
R^2 = x^2+y^2
=(16n^2+8n-3)^2/(4n^2+2n)^2 +1/(4n^2)
=(32n^3+16n^2-8n-1)/ (8n^3+4n^2)
当n趋向于无穷大,R^2= 32/8=4
所以面积为piR^2 = 4pi