Uma circunferência muito especial ...

Antes de começares a tarefa altera as configurações na roda dentada[img width=20,height=25]data:image/png;base64,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[/img] para “Rotular: Apenas para pontos novos”. Para tal acede às três linhas horizontais [img width=25,height=23]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAlCAYAAAAwYKuzAAAAAXNSR0IArs4c6QAAAKhJREFUWEftl80JwCAMhXUXHcZhnMZhHEYH8dbirVCQlKcQ7fOcF8OXP7WttcsoPpYBgtkhQRCg2ZtgKcXknFEIIn0IwXjvX7ZDgj3AlJLoAtQoxnhogLVWFI5I75z7TlDkebHR3l28GI7IPQmKMA2M9ibIQf1I7ZmbBC3wGfq9m2QGAdQHCf6bYB/Uqt+D3CQzNonqXx3agTP0nIMoRRIkQZQAqldfgzdw/NKJMcXQAQAAAABJRU5ErkJggg==[/img] no canto superior direito.
Parte 1
- Constrói um triângulo [ABC].[br]Sugestão: recorre ao menu  para a construção do triângulo na opção [img width=29,height=33]data:image/png;base64,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[/img][br][br]- Constrói os pontos médios dos lados desse triângulo e renomeia-os para M1, M2 e M3.[br]Sugestão: recorre ao menu [img width=29,height=28]data:image/png;base64,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[/img] e seleciona o comando correspondente.[br][br]- Constrói as retas suporte dos lados do triângulo [ABC] e as alturas do triângulo.[br]Sugestão: recorre ao menu [img width=24,height=21]data:image/png;base64,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[/img] e [img width=23,height=21]data:image/png;base64,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[/img] e seleciona o comando correspondente.[br][br] - Marca os pés das alturas e renomeia-os para P1, P2 e P3. [br][br]- Constrói o ortocentro do triângulo [ABC], renomeia-o para ort.[br][br]- Esconde as alturas e coloca a tracejado as retas suporte dos lados (clica sobre elas com o botão direito do rato).[br][br]- Constrói a circunferência que passa por P1, P2 e P3.[br]Sugestão: recorre ao menu [img width=33,height=30]data:image/png;base64,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[/img]e seleciona o comando correspondente.[br][br]- Constrói os pontos médios dos segmentos que unem o ortocentro aos vértices do triângulo [ABC].
De todos os pontos criados nesta figura, quantos deles pertencem à circunferência? Que pontos são esses?
Arrasta os vértices do teu triângulo. O que observas? Formula conjeturas a partir das tuas observações.
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Information: Uma circunferência muito especial ...