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.
Sebi said data, emails and other documents are being retrieved from the seized devices and detailed investigation is in progress. Russians and Ukrainians are both prolific users of Telegram. They rely on the app for channels that act as newsfeeds, group chats (both public and private), and one-to-one communication. Since the Russian invasion of Ukraine, Telegram has remained an important lifeline for both Russians and Ukrainians, as a way of staying aware of the latest news and keeping in touch with loved ones. These entities are reportedly operating nine Telegram channels with more than five million subscribers to whom they were making recommendations on selected listed scrips. Such recommendations induced the investors to deal in the said scrips, thereby creating artificial volume and price rise. In 2014, Pavel Durov fled the country after allies of the Kremlin took control of the social networking site most know just as VK. Russia's intelligence agency had asked Durov to turn over the data of anti-Kremlin protesters. Durov refused to do so. 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.
from nl
