Diagonais de um vértice no polígono regular

¯\_(ツ)_/¯ O que são DIAGONAIS?
Diagonal é a linha reta que permite unir dois vértices que não são contíguos de um poliedro ou de um polígono. As diagonais aparecem como segmentos ou retas que apresentam uma determinada inclinação.
Desenhando para entender conceitos matemáticos \^o^/
[list=1][*] Com a ferramenta polígono regular [img]data:image/png;base64,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[/img] construa três polígonos com quantidades diferentes de lados [br][/*][*]Com a ferramenta ponto médio [img]data:image/png;base64,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[/img] determine o centro do polígono[/*][*]Construa então as três circunferências circunscritas aos respectivos polígonos com a ferramenta círculo definido por centro e ponto [img]data:image/png;base64,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[/img][/*][*]Após ler a definição de diagonal, utilize a ferramenta [img]data:image/png;base64,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[/img] para desenhar as diagonais que partem de um dos vértices do polígono[/*][/list]
Contando diagonais
Obrigada especial aos professores Jorge Cassio, Sérgio Dantas e Gustavo Reis. Essa atividade foi desenvolvida com base nos materiais e construções geométricas desenvolvidas e generosamente disponibilizadas por vocês entusiastas da matemática.

Information: Diagonais de um vértice no polígono regular