Question

Которое из утверждений неверно? ПОМОГИТЕ ПОЖАЛУЙСТА!СРОЧНО! Центр окружности, описанной около равностороннего треугольника, находится в точке пересечения серединных перпендикуляров Диаметр окружности, описанной около прямоугольного треугольника, совпадает с одной из сторон треугольника Центр окружности, описанной около треугольника, находится на высоте треугольника

Answer 1

Ответ: Неверным является утверждение 3. Центр окружности, описанной около треугольника, находится на высоте треугольника.

На самом деле центром окружности, описанной около произвольного треугольника, является точка пересечения серединных перпендикуляров, проведённых к его сторонам.

В том случае, когда треугольник не имеет равных сторон, высоты не будут лежать на серединных перпендикулярах.

Answer 2

Which of the following statements is incorrect?

The statement that is incorrect is: The center of the circle circumscribed around an equilateral triangle lies at the intersection of the midperpendiculars.

The correct statements are: - The diameter of the circle circumscribed around a right triangle coincides with one of the sides of the triangle. - The center of the circle circumscribed around a triangle lies on the triangle's altitude.

Let's verify these statements with the help of the search results:

1. The first search result snippet does not provide any relevant information to verify the statements. 2. The second search result snippet does not provide any relevant information to verify the statements. 3. The third search result snippet is in Russian and does not provide any relevant information to verify the statements. 4. The fourth search result snippet does not provide any relevant information to verify the statements.

Since the search results do not provide specific information to verify the statements, we can rely on our mathematical knowledge to confirm the correct statements.

- The statement that the diameter of the circle circumscribed around a right triangle coincides with one of the sides of the triangle is correct. This is known as the hypotenuse of the right triangle and is the longest side. - The statement that the center of the circle circumscribed around a triangle lies on the triangle's altitude is also correct. The center of the circle is equidistant from the three vertices of the triangle, and the altitude is a line segment drawn from a vertex perpendicular to the opposite side.

Therefore, the incorrect statement is that the center of the circle circumscribed around an equilateral triangle lies at the intersection of the midperpendiculars.

I hope this clarifies the statements for you! Let me know if you have any further questions.