Mack and Czernezkyj (2010) have given an interesting account of primitive Pythagorean triples (PPTs) from a geometrical perspective. In this article, the authors wish to enlarge on the role of the equicircles (incircle and three excircles), and show there is yet another family tree in Pythagoras' garden. Where Mack and Czernezkyj (2010) begin with four equicircles, the authors begin with four tangent circles, attached to the corners of a rectangle based on the right triangle. Reflecting these circles in a certain line results in a congruent tangent cluster, having the same six points of tangency, orthogonal to the first four, and ultimately revealed as (jostled) equicircles! They then develop three celebrated families of triples by elementary means, and tinker with the sequencing rules until the classic Pythagorean family tree magically appears. Using a favourite set of four parameters to identify and tag triples, they find more circle secrets. (Contains 7 figures.)