Golden Rectangles in a Right Triangle

This construction was created by experimenting with the Geogebra interactive geometry application. I began with the right-triangle with side lengths 3, 4, and 5. Then I constructed its incircle, which has unit radius. In each of the three corners I inscribed a smaller circle, tangent to the incircle. Considering the circle inscribed in the 3-5 corner, I observed that the numerical value of its radius is 1/φ², where φ (phi) is the golden ratio, equal to (1+√5)/2. This enables construction of three golden rectangles as shown. The dimensions of the rectangles are 1/φ² x 1/φ, 1/φ x 1, and 1 x φ.