Triangle formed by a hyperbola's tangent and asymptotes

Here is a "GeoGebra proof" that the area of the triangle formed by the two oblique asymptotes of a hyperbola of the form (x/a)^2 - (y/b)^2 = 1 and a tangent to the hyperbola is equal to the product of a and b. Drag the diamond shaped point on the x-axis to move the point of tangency (point A).