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Очень красивая задача с командной олимпиады сеньоров с Колма, который идет прямо сейчас.
Биссектрисы AA1, BB1, CC1 неравнобедренного треугольника ABC пересекаются в точке I. Впи-
санная окружность треугольника ABC касается стороны BC в точке A2. Окружность ωa проходит
через точки A1, A2 и середину отрезка AI. Окружности ωb и ωc определяются аналогично. Докажите,
что центры окружностей ωa, ωb, ωc лежат на одной прямой.



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Очень красивая задача с командной олимпиады сеньоров с Колма, который идет прямо сейчас.
Биссектрисы AA1, BB1, CC1 неравнобедренного треугольника ABC пересекаются в точке I. Впи-
санная окружность треугольника ABC касается стороны BC в точке A2. Окружность ωa проходит
через точки A1, A2 и середину отрезка AI. Окружности ωb и ωc определяются аналогично. Докажите,
что центры окружностей ωa, ωb, ωc лежат на одной прямой.

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Telegram | DID YOU KNOW?

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At the start of 2018, the company attempted to launch an Initial Coin Offering (ICO) which would enable it to enable payments (and earn the cash that comes from doing so). The initial signals were promising, especially given Telegram’s user base is already fairly crypto-savvy. It raised an initial tranche of cash – worth more than a billion dollars – to help develop the coin before opening sales to the public. Unfortunately, third-party sales of coins bought in those initial fundraising rounds raised the ire of the SEC, which brought the hammer down on the whole operation. In 2020, officials ordered Telegram to pay a fine of $18.5 million and hand back much of the cash that it had raised. READ MORE The SC urges the public to refer to the SC’s I nvestor Alert List before investing. The list contains details of unauthorised websites, investment products, companies and individuals. Members of the public who suspect that they have been approached by unauthorised firms or individuals offering schemes that promise unrealistic returns Pavel Durov, a billionaire who embraces an all-black wardrobe and is often compared to the character Neo from "the Matrix," funds Telegram through his personal wealth and debt financing. And despite being one of the world's most popular tech companies, Telegram reportedly has only about 30 employees who defer to Durov for most major decisions about the platform. Oh no. There’s a certain degree of myth-making around what exactly went on, so take everything that follows lightly. Telegram was originally launched as a side project by the Durov brothers, with Nikolai handling the coding and Pavel as CEO, while both were at VK.
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