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.
Oleksandra Matviichuk, a Kyiv-based lawyer and head of the Center for Civil Liberties, called Durov’s position "very weak," and urged concrete improvements. Recently, Durav wrote on his Telegram channel that users' right to privacy, in light of the war in Ukraine, is "sacred, now more than ever." Unlike Silicon Valley giants such as Facebook and Twitter, which run very public anti-disinformation programs, Brooking said: "Telegram is famously lax or absent in its content moderation policy." Perpetrators of such fraud use various marketing techniques to attract subscribers on their social media channels. As a result, the pandemic saw many newcomers to Telegram, including prominent anti-vaccine activists who used the app's hands-off approach to share false information on shots, a study from the Institute for Strategic Dialogue shows.
from tw
