Golden section and yin-yang symbol proportions

[tongtu]

Hello, dear friends of mathhelpboards;

I stumbled with a striking claim in https://www.cut-the-knot.org/do_you_know/GoldenRatioInYinYang.shtml

Sorry, I couldn't paste the pic. The question is if there is an algebraical or trig proof for this claim, as the angle seems to be just 45º. Then, is there an EXACT proof for this claim?

 

[Greg]

What angle are you referring to? What do you mean by an "exact" proof?

 

[tongtu]

What angle are you referring to? What do you mean by an "exact" proof?

Sorry, I got it. The solution is now in Cut the knot. Assuming, AB=1, AE=12 and BE=5‾√2. It follows that

BI=5‾√2+12=φ

BH=5‾√2−12=φ−1.

Problem solved! Thanks and sorry again.