Five similar triangles

Take the arbitrary scalene triangle ABC. On side AB take the arbitrary point D.
Find (by construction) the two points I, J (on side AC), and two points K, L (on side AC), such that
five triangles ABC, AJD, ADI, BDK, and BLD all are similar.

Construction:

1. The segments JD and DK are parallel to sides CB and AC, respectively.
2. Draw the circle through three points CDB. The point of intersection of the circle with side AC gives the point I.
3. Draw the circle through three points CDA. The point of intersection of the circle with side BC gives the point L.