Let`s assume that points M, N and P are the touching points of those 3 circles: Then: Y M + M Z = 14, Z N + N X = 20 X P + P Y = 18 And also: M Z = ZN, Y M = P Y and N X = X P. Now we have a system of 3 equations ( Y M, M Z and X P are the radii of each circle ): Y M + M Z = 14 M Z + X P = 20 X P + Y M = 18 ------------------------ - Y M - M Z = - 14 + X P + Y M = 18 ------------------------ X P - M Z = 4 ----------------------- - Y M - M Z = - 14 + M Z + X P = 20 ------------------------ X P - Y M = 6 /* ( - 1 ) X P - M Z = 4 -------------------------- - X P + Y M = - 6 X P - M Z = 4 ------------------------ Y M - M Z = - 2 Y M + M Z = 14 ----------------------- 2 Y M = 12 => Y M = 6 M Z - 6 = 2 => M Z = 8 X P + 6 = 18 => X P = 12 Answer: Radii of the circles are: 12, 8 and 6.
