Problem: The image a of a circle on a plane π is given, as well as the image c of its center.  You also see the image of a point P lying on π.  Consider an arbitrary image line h through c, and set a 2D reference frame on π such that its x axis projects to h.  Provided that the radius of the circle is known, how can you find the coordinates of P in the reference frame we just defined?

Solution sketch: h crosses the image of the circle it two points p₁ and p₂; let t₁ and t₂ be the tangents to c in p₁ and p₂: they can be interpreted as the projections of two parallel lines on π, perpendicular to the x axis of the defined reference frame.  t₁ and t₂ intersect at a vanishing point v_y, which represents the direction of the y axis.  By connecting v_y to c, you find two intersections with a; by intersecting the tangents to c at these two points, you find the vanishing point v_x, direction of the x axis.  You can therefore find P's projection on the x axis and on the y axis in the image, then measure coordinates by means of the cross-ratio.