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Дано трикутник АВС, точки D та Е на його сторонах задовольняють умову BD = EC. Пряма DE перетинає пряму ВС в точці F, а точка N — середина дуги ВАС описаного колa трикутника ABC. Точка Х — інцентр трикутника ECF, а точка Y — центр зовнівписаного кола DBF.
Доведіть, що NX = NY.



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Дано трикутник АВС, точки D та Е на його сторонах задовольняють умову BD = EC. Пряма DE перетинає пряму ВС в точці F, а точка N — середина дуги ВАС описаного колa трикутника ABC. Точка Х — інцентр трикутника ECF, а точка Y — центр зовнівписаного кола DBF.
Доведіть, що NX = NY.

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