The following figure points out that like the circle 3 fills the dis­tance from below the triangle’s base, to bottom of the outer circle 1, the circle 2 does the same on to the other side from above the base, which shows us with ease that the height of the Triangle is even in Phi ratio with the outer circle diameter!

This revealed an alternative way to draw the complete golden triangle - all its sides being involved - and instructs us of many interesting detais con­cern­ing the relations between our ‘el­e­men­ta­ry’ rec­tan­gle and the con­cen­tric circles scaled in Golden Ratio, which look like to have beeen pre­sent behind the scenes at each step of our process, giving rise to what we can settle from now on as the “Golden Circles Ratio.

the Kepler's cite “division of a line into extreme and mean ratio” it was thus o­ver­come,
as not only linear.
In deed a golden expansion map
is defined by a se­quence of con­cen­tric waves, whose di­am­e­ters are reg­u­lat­ed by increase of the golden ratio j power – tap the figure if HTML.

The next step dis­closes one still un­known gold­en spi­ral, which works out through this plan, ie. cros­sing eve­ry cir­cle at the same [zero] degree.
Our Great Triangle handles all these and much more, like a gate be­tween the plain for­mu­las and the revolving energy!