Telegram Group & Telegram Channel
Задача 51:
Автор - Пучков Пëтр

Обобщение леммы 255

P₁ и P₂ - изогонально сопряжены в треугольнике ABC. X₁ и X₂ - проекции B на AP₁ и AP₂, а Y₁ и Y₂ - проекции B на CP₁ и CP₂ соответственно.

1) Точки X₁ и X₂, Y₁ и Y₂ симметричны относительно средней линии треугольника ABC. Если P₁ и P₂ совпадают (случай инцентра), то X₁ = X₂, Y₁ = Y₂ лежат на средней линии.

2) Обобщённые точки 255 лежат на хордах педальной окружности точек P₁ и P₂. Если A₁, B₁, C₁ и A₂, B₂, C₂ - проекции точек P₁ и P₂ на стороны BC, AC и AB треугольника соответственно, то X₁ ∈ A₁B₂, X₂ ∈ A₂B₁, Y₁ ∈ B₂C₁, Y ∈ B₁C₂.



group-telegram.com/NeuroGeometry/74
Create:
Last Update:

Задача 51:
Автор - Пучков Пëтр

Обобщение леммы 255

P₁ и P₂ - изогонально сопряжены в треугольнике ABC. X₁ и X₂ - проекции B на AP₁ и AP₂, а Y₁ и Y₂ - проекции B на CP₁ и CP₂ соответственно.

1) Точки X₁ и X₂, Y₁ и Y₂ симметричны относительно средней линии треугольника ABC. Если P₁ и P₂ совпадают (случай инцентра), то X₁ = X₂, Y₁ = Y₂ лежат на средней линии.

2) Обобщённые точки 255 лежат на хордах педальной окружности точек P₁ и P₂. Если A₁, B₁, C₁ и A₂, B₂, C₂ - проекции точек P₁ и P₂ на стороны BC, AC и AB треугольника соответственно, то X₁ ∈ A₁B₂, X₂ ∈ A₂B₁, Y₁ ∈ B₂C₁, Y ∈ B₁C₂.

BY NeuroGeometry




Share with your friend now:
group-telegram.com/NeuroGeometry/74

View MORE
Open in Telegram


Telegram | DID YOU KNOW?

Date: |

Ukrainian forces have since put up a strong resistance to the Russian troops amid the war that has left hundreds of Ukrainian civilians, including children, dead, according to the United Nations. Ukrainian and international officials have accused Russia of targeting civilian populations with shelling and bombardments. There was another possible development: Reuters also reported that Ukraine said that Belarus could soon join the invasion of Ukraine. However, the AFP, citing a Pentagon official, said the U.S. hasn’t yet seen evidence that Belarusian troops are in Ukraine. "Someone posing as a Ukrainian citizen just joins the chat and starts spreading misinformation, or gathers data, like the location of shelters," Tsekhanovska said, noting how false messages have urged Ukrainians to turn off their phones at a specific time of night, citing cybersafety. In the United States, Telegram's lower public profile has helped it mostly avoid high level scrutiny from Congress, but it has not gone unnoticed. Asked about its stance on disinformation, Telegram spokesperson Remi Vaughn told AFP: "As noted by our CEO, the sheer volume of information being shared on channels makes it extremely difficult to verify, so it's important that users double-check what they read."
from ye


Telegram NeuroGeometry
FROM American