I have the triangle ABC and an unknown point P not necessarily inside the triangle. Also, I have three lengths (d1, d2, d3) with the same ratio of lengths PA, PB, and PC. The question is does P exist?
$\frac{d1}{PA} = \frac{d2}{PB} = \frac{d3}{PC}$
I already know that the locus of points with fixed distance ratio from points A and B is a circle with centre laid on the extension of AB (or in one case a line). But, what is the constraint on the distance ratios of P with respect to A, B, and C, for P to exist?