Question

Которое из утверждений неверно? Центр окружности, вписанной в треугольник, находится на пересечении его биссектрис Диаметр окружности, описанной около прямоугольного треугольника, совпадает с одной из сторон треугольника Центр окружности, описанной около равностороннего треугольника, находится в точке пересечения средних линий

Answer 1

ответ 3 Центр окружности

Answer 2

Which of the following statements is incorrect?

The statements provided are related to circles inscribed in triangles and circles circumscribed around triangles. Let's evaluate each statement:

1. The center of the circle inscribed in a triangle lies at the intersection of its angle bisectors. 2. The diameter of the circle circumscribed around a right triangle coincides with one of the triangle's sides. 3. The center of the circle circumscribed around an equilateral triangle lies at the intersection of the triangle's medians.

To determine which statement is incorrect, we will examine each one in turn.

Statement 1: The center of the circle inscribed in a triangle lies at the intersection of its angle bisectors.

This statement is correct. According to the properties of an inscribed circle, the center of the circle is equidistant from all three sides of the triangle. This means that the center must lie at the intersection of the angle bisectors of the triangle.

Statement 2: The diameter of the circle circumscribed around a right triangle coincides with one of the triangle's sides.

This statement is incorrect. In a right triangle, the hypotenuse is the side opposite the right angle. The diameter of the circle circumscribed around the right triangle is equal to the length of the hypotenuse, not one of the triangle's sides.

Statement 3: The center of the circle circumscribed around an equilateral triangle lies at the intersection of the triangle's medians.

This statement is correct. In an equilateral triangle, the medians intersect at a point called the centroid. The center of the circle circumscribed around the equilateral triangle coincides with the centroid, which is the point of intersection of the medians.

Based on the evaluation of each statement, Statement 2 is incorrect.

Therefore, the incorrect statement is: "The diameter of the circle circumscribed around a right triangle coincides with one of the triangle's sides."

Please let me know if there's anything else I can help you with!