You haven't described your variables or whether you're casting a ray, or whether you're only trying to determine the closest point in the triangle to the test point closer than "offset."

IF you're only trying to determine the closest point closer than a given offset (or radius? a sphere-triangle intersection, for instance) -

You can calculate the point-in-plane as:

// vecNormal must be normalized. I.e., a unit vector
// if you're not interested in the distance to the point, remove the use of float* out_distance
bool PointCloserThanOffset( D3DXVECTOR3 vecTestPoint, D3DXVECTOR3 vecPointOnPlane, D3DXVECTOR3 vecNormal, float offset,
   float *out_distance, D3DXVECTOR3 *out_pointInPlane)
{
   // create a vector from the test point to any point in the plane
   D3DXVECTOR3 vecTemp(vecTestPoint - vecPointOnPlane);
   // calculate the distance from the test point to the plane
   float distance = D3DXVec3Dot(&vecTemp, &vecNormal);
   if( distance > offset ) return false;
   *out_distance = distance;
   *out_pointInPlane = vecTestPoint + vecNormal * distance;
   return true;
}
...
// use the function
float distance;
D3DXVECTOR3 pointInPlane;
if( PointCloserThanOffset( vecTestPoint, vecPointOnPlane, vecNormal, offset, &distance, &pointInPlane )
{
   // if desired, make further tests on "distance." Not sure what the intent of your collision test is.
   // do your barycentric coord test here using D3DXVECTOR3 pointInPlane
}

If desired, you can add to the PointCloserThanOffset function:

if( fabs(distance) < EPSILON) distance = 0;

For ray triangle intersection (I combine plane and triangle intersection) I use an implementation of the Moller-Trumbore algorithm which uses two cross-products. Many algorithms use 3 cross-products, so M-B may be slightly faster in that regard.

It collide with the traingle when
1.) it is on the triangle plane in area ABC
or
2.) it is on negative half space of triangle plane and line from point perpendicular to triangle plane is inside area ABC

I don't have any "ray direction" attributable to any object.

You mention "line from point perpendicular to triangle plane." Is that not a direction? Your collision criteria 2) is a ray-cast from the point to the plane parallel to the plane normal. If I understand your intent - if distance is <=0, the direction is the plane normal.

You previously posted your criteria for a collision.

Hi

My aim is to calculate if a point P(x,y,z) collide with a traingle described by A(x,y,z),B(x,y,z) and C(x,y,z). It collide with the traingle when

1.) it is on the triangle plane in area ABC

or

2.) it is on negative half space of triangle plane and line from point perpendicular to triangle plane is inside area ABC

Is that, in fact, your criteria? If it is, then, along with the distance calc posted above, casting a ray from the point in the direction of the triangle normal will provide you with results to determine 1) and 2).

it is not ray direction because between two frames the movement direction might be not perpendicular to the triangle plane. ... between two frames the movement direction ... And this value I should introduce into "D" parameter, am I right???

Movement of what?? You've said nothing previously about "frames" or a moving object. If what you previously posted is NOT your criteria for collision, and you're asking for help with something, you'll have to clearly describe the problem you're trying to solve.