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№17 (Полный четырехсторонник)

Дана четверка прямых общего положения

Доказать, что:
а) Окружности (BDE), (ABC), (ADF) и (CEF) пересекаются в одной точке (точка Микеля)

b) Центры окружностей (BDE), (ABC), (ADF) и (CEF) лежат на одной окружности с точкой микеля

c) Середины диагоналей полного четырезсторонника лежат на одной прямой (прямая Гаусса)

d) Ортоцентры треугольников (BDE), (ABC), (ADF) и (CEF) лежат на одной прямой (прямая Обера)

e) Прямая Гаусса перпендикулярна прямой Обера (теорема Гаусса-Боденмиллера)

https://www.geogebra.org/m/zg4wtmrj

Если вы знаете еще замечательные факты про полный четырехсторонник, будет очень здорово, если вы ими поделитесь @geomweeklyauthor

Geometry Weekly
№17 (Полный четырехсторонник)

Дана четверка прямых общего положения

Доказать, что:
а) Окружности (BDE), (ABC), (ADF) и (CEF) пересекаются в одной точке (точка Микеля)

b) Центры окружностей (BDE), (ABC), (ADF) и (CEF) лежат на одной окружности с точкой микеля

c) Середины диагоналей полного четырезсторонника лежат на одной прямой (прямая Гаусса)

d) Ортоцентры треугольников (BDE), (ABC), (ADF) и (CEF) лежат на одной прямой (прямая Обера)

e) Прямая Гаусса перпендикулярна прямой Обера (теорема Гаусса-Боденмиллера)

https://www.geogebra.org/m/zg4wtmrj

Если вы знаете еще замечательные факты про полный четырехсторонник, будет очень здорово, если вы ими поделитесь @geomweeklyauthor
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How to Use Bitcoin?

n the U.S. people generally use Bitcoin as an alternative investment, helping diversify a portfolio apart from stocks and bonds. You can also use Bitcoin to make purchases, but the number of vendors that accept the cryptocurrency is still limited. Big companies that accept Bitcoin include Overstock, AT&T and Twitch. You may also find that some small local retailers or certain websites take Bitcoin, but you’ll have to do some digging. That said, PayPal has announced that it will enable cryptocurrency as a funding source for purchases this year, financing purchases by automatically converting crypto holdings to fiat currency for users. “They have 346 million users and they’re connected to 26 million merchants,” says Spencer Montgomery, founder of Uinta Crypto Consulting. “It’s huge.”

№17 (Полный четырехсторонник)

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