Question

如图,直线y=1/2x+2分别与x轴、y轴交于A、B两点,P是线段AO上一个动点,以OP为半径的圆O与y轴正半轴交于M,

Answer 1

由题意可设P(-p,0),N(-n,2-(1/2)n),则有

-n-(-p)=2-(1/2)n ==> p=2+(1/2)n

PM=√2OP=√2p=√2[2+(1/2)n]

PN=√2[2-(1/2)n]

PM+PN=√2[2+(1/2)n]+√2[2-(1/2)n]=4√2