The circle x 2+y 2 =1,the center of which is the origin o (0,0), and the radius r= 1.

The straight line y=kx+ 1 intersects the circle x 2+y 2 =1at two points p and q,

Angle POQ= 120 degrees.

Then the distance from O to PQ is d= 1/2.

According to the distance formula from point to straight line

1/√(k？ + 1)= 1/2

∴k？ =3,

∴k= √3