Vector AC=(ksinθ-8, t), which consists of vector AC and vector a*** straight line, AC=ma, (m is a constant).

That is, (ksinθ-8)/(- 1) = t/2, 2ksinθ =16-t.

Therefore, 16-t = 2ksinθ > 8sinθ, and if any θ range is 0 ≤ θ≤π/2, then 16-t > 8.

So t < 8, and the maximum value of tsinθ is 4, so t = 4.

When t=4, 2ksinθ= 16-t and ksinθ=6, so the vector AC = (-2,4), c (6,4).

So AC. OC=-2×6+4×4=4。

When t=-4, since 2ksinθ= 16-t and ksinθ= 10, the vector AC=(2, -4), C( 10, -4).

So AC. OC=2× 10+(-4)×(-4)=36。