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а тепер така нормальна по обсягу добірка на трикутник a=(b²+c²)/(b+c)
1. жергоніана і симедіана співпадають
2. триполяра інцентра паралельна симедіані
3. точка фейєрбаха лежить на медіані
4. X(7)X(8) || BC
5. OI ⊥ жергоніані
6. описаний еліпс з центром X(9) проходить через перетин медіани з (ABC)
7. точка дотику напівзовнівписаного кола - фокус вписаної параболи з директорисою X(4)X(8)
8. середина дуги BC - фокус вписаної параболи з директорисою X(4)X(9)
9. пряма із вершини A через точку шиффлера проходить через точку штейнера

Олимпиадная геометрия
Forwarded from скучні задачі (Дон Шихуан)
а тепер така нормальна по обсягу добірка на трикутник a=(b²+c²)/(b+c)
1. жергоніана і симедіана співпадають
2. триполяра інцентра паралельна симедіані
3. точка фейєрбаха лежить на медіані
4. X(7)X(8) || BC
5. OI ⊥ жергоніані
6. описаний еліпс з центром X(9) проходить через перетин медіани з (ABC)
7. точка дотику напівзовнівписаного кола - фокус вписаної параболи з директорисою X(4)X(8)
8. середина дуги BC - фокус вписаної параболи з директорисою X(4)X(9)
9. пряма із вершини A через точку шиффлера проходить через точку штейнера
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а тепер така нормальна по обсягу добірка на трикутник a=(b²+c²)/(b+c)

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