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 regulator said it has been undertaking several campaigns to educate the investors to be vigilant while taking investment decisions based on stock tips. This provided opportunity to their linked entities to offload their shares at higher prices and make significant profits at the cost of unsuspecting retail investors. These administrators had built substantial positions in these scrips prior to the circulation of recommendations and offloaded their positions subsequent to rise in price of these scrips, making significant profits at the expense of unsuspecting investors, Sebi noted. After fleeing Russia, the brothers founded Telegram as a way to communicate outside the Kremlin's orbit. They now run it from Dubai, and Pavel Durov says it has more than 500 million monthly active users. I want a secure messaging app, should I use Telegram?
from vn
