Solution. Let G be the sphere with center O that contains the base circle of the cone. Let P' be the intersection of G with the ray OP, and let I be the point of G, diametrically opposite with P'.
Apply inversion to the sphere with center I and radius IP'. The image of G is the tangent plane S at point P'. The image of the base circle is some circle k in the plane S.
Let X1' and X2' be the images of X1 and X2, respectively. The points P',X1',X2' are collinear, moreover X1',X2' lie on k. Then
The numerator, being the power of P' with respect to k, does not depend on the points X1',X2'.