if the transversal Y = mrx ; r = 123 cut offs equal intercepts on the transversal x+y=1 then
1+m1, 1+m2 , 1+m3 are in AP , GP or HP
Point of intersection of y=mx with x+y=1 is of the type, (1/M, m/M) where M=1+m.
(1/M2, m2/M2) is the midpoint of (1/M1, m1/M1) & (1/M3, m3/M3) and hence...
1/M2=(1/M1+1/M3)/2. HP.