When at the optimum combination of two inputs, the isocost curve and isoquant curve are tangent. The tangential point is the optimum solution. So obviously A is correct.
At this given output (which is decided by the given isoquant curve), the isocost curve is the minimum cost that can achieve this production level.
This option is a little tricky. Think about the concept of tangency. Any isocost line(share same slope with the tangential line) that has intersection points with the given isoquant curve will at least be above the tangential line.(which means a higher cost.)
So B is correct.
The slope of isoquant curve is equal to marginal rate of technical substitution, while the slope of isocost curve is equal to the ratio of input prices. So according to A, C is just another way to express this idea. C is also correct.
The correct answer is D.