Problema de Apolonio: dibujar dos circunferencias tangentes a otras tres de distintos radios

Technical Drawing Course: https://educale.com There are eight solutions: one inner circle, one outer circle, and six mixed circles. We reduce the radius of the smallest circle in the other two. We draw the new auxiliary circles. Now we have to find the centers of the circles tangent to two other circles and passing through a point. We join the centers of these two circles. Through them, we draw two parallel lines in any direction. The points of intersection are joined to find the center of inversion M. M is joined to O1. By joining the centers, two points of intersection R and S are generated. We draw a circle that passes through points R, S, and O1, drawing two perpendicular bisectors. This circle O4 intersects line M with O1, at its inverse O'1. The problem that now arises is to draw the circles that pass through points O1 and O'1 and are tangent to one of the two auxiliary circles. The points of intersection of circle O4 with one of the auxiliary circles are joined to find point P on the line connecting the two points. From P, the points of tangency to the auxiliary circle are drawn. The perpendicular bisector of points O1 and O'1 is drawn, and the solution centers will lie on this bisector. These are found by joining center O2 with its points of tangency. To locate all the points of tangency, the two solution centers are joined with the three given centers. The two solution circles are then drawn.