# Golden Ratio In A Pentagon

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Illustration showing how the golden ratio in a regular pentagon (inscribed in a circle) can be found using Ptolemy’s theorem. The lines that are bolded form a quadrilateral. Ptolemy’s theorem says the square of b equals the sum of a squared and ab, which in turn gives the golden ratio.

### Keywords

circle, ptolemy, inscribed, circumscribed, golden ratio, golden mean, golden proportion, golden section, extreme ratio, mean ratio, medial section, golden cut, divine section, regular pentagon, Ptolemy's theorem### Galleries

Golden Mean### Source

Florida Center for Instructional Technology *Clipart ETC* (Tampa: University of South Florida, 2007)

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