Two tangents are drawn from the point \( P(-1,1) \) to the circle \( x^2 + y^2 - 2x - 6y + 6 = 0 \). If these tangents touch the circle at points \( A \) and \( B \), and if \( D \) is a point on the circle such that length of the segments \( AB \) and \( AD \) are equal, then the area of triangle \( ABD \) is equal to:
