Через середины сторон треугольника проведены три синие параллельные прямые. Докажите, что прямые, симметричные сторонам относительно соответствующих синих прямых, пересекаются в одной точке. Найдите геометрическое место точек пересечения.
Ничего не значащий спойлер:
If we call the Minkowski perpendicular bisector of a segment with slope a the line through its midpoint with slope 1/a (the two lines are orthogonal in the Minkowski metric), the Klehr-Bliss theorem says that the Minkowski perpendicular bisectors of the three sides of a triangle are concurrent. The proof follows the usual proof: any point on the Minkowski perpendicular bisector of a segment is Minkowski equidistant from the two ends.
Через середины сторон треугольника проведены три синие параллельные прямые. Докажите, что прямые, симметричные сторонам относительно соответствующих синих прямых, пересекаются в одной точке. Найдите геометрическое место точек пересечения.
Ничего не значащий спойлер:
If we call the Minkowski perpendicular bisector of a segment with slope a the line through its midpoint with slope 1/a (the two lines are orthogonal in the Minkowski metric), the Klehr-Bliss theorem says that the Minkowski perpendicular bisectors of the three sides of a triangle are concurrent. The proof follows the usual proof: any point on the Minkowski perpendicular bisector of a segment is Minkowski equidistant from the two ends.
One thing that Telegram now offers to all users is the ability to “disappear” messages or set remote deletion deadlines. That enables users to have much more control over how long people can access what you’re sending them. Given that Russian law enforcement officials are reportedly (via Insider) stopping people in the street and demanding to read their text messages, this could be vital to protect individuals from reprisals. "We're seeing really dramatic moves, and it's all really tied to Ukraine right now, and in a secondary way, in terms of interest rates," Octavio Marenzi, CEO of Opimas, told Yahoo Finance Live on Thursday. "This war in Ukraine is going to give the Fed the ammunition, the cover that it needs, to not raise interest rates too quickly. And I think Jay Powell is a very tepid sort of inflation fighter and he's not going to do as much as he needs to do to get that under control. And this seems like an excuse to kick the can further down the road still and not do too much too soon." In a statement, the regulator said the search and seizure operation was carried out against seven individuals and one corporate entity at multiple locations in Ahmedabad and Bhavnagar in Gujarat, Neemuch in Madhya Pradesh, Delhi, and Mumbai. The Dow Jones Industrial Average fell 230 points, or 0.7%. Meanwhile, the S&P 500 and the Nasdaq Composite dropped 1.3% and 2.2%, respectively. All three indexes began the day with gains before selling off. Telegram, which does little policing of its content, has also became a hub for Russian propaganda and misinformation. Many pro-Kremlin channels have become popular, alongside accounts of journalists and other independent observers.
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