问题
填空题
已知圆O的半径为1，PA、PB为该圆的两条切线，A、B为两切点，那么
|
答案
设PA与PO的夹角为a，则|PA|=|PB|=1 tanα
y=
•PA
=|PB
||PA
|cos2αPB
=
•cos2α=1 (tanα)2
•cos2αcos2α sin2α
=
•cos2α1+cos2α 1-cos2α
记cos2a=u．则y=
=(-u-2)+u(u+1) 1-u
=-3+(1-u)+2 1-u 2 1-u
≥-3+22
即
•PA
的最小值为-3+2PB 2
故答案为：-3+22