Golden Ratio in Circles

Problem 1

Golden Ratio in Circles,problem 1,problem

Solution to Problem 1

Taking the common radius of the two circles to be $1,$ $CD=2,$ $BD=\sqrt{5},$ $BE=\sqrt{5}+1,$ whereas $AB=2.$

Problem 2

Golden Ratio in Circles,problem 2,problem

Solution to Problem 2

$HK$ equals $BE$ from Problem 1. $KG=AB.$

Golden Ratio in Circles,problem 2,solution

Acknowledgment

This page is a variation on a construction by Thanos Kalogerakis.

 

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