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.
The Securities and Exchange Board of India (Sebi) had carried out a similar exercise in 2017 in a matter related to circulation of messages through WhatsApp. The Russian invasion of Ukraine has been a driving force in markets for the past few weeks. "He has kind of an old-school cyber-libertarian world view where technology is there to set you free," Maréchal said. The message was not authentic, with the real Zelenskiy soon denying the claim on his official Telegram channel, but the incident highlighted a major problem: disinformation quickly spreads unchecked on the encrypted app. The fake Zelenskiy account reached 20,000 followers on Telegram before it was shut down, a remedial action that experts say is all too rare.
from ua
