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МатематикаВопрос:
A circle can be circumscribed around a quadrilateral.
Ответ:
Ответ:
1. Не всегда
Обоснование:
Около четырехугольника можно описать окружность только в том случае, если сумма его противоположных углов равна 180 градусам (теорема Птолемея). Не всякий четырехугольник обладает этим свойством. Например, вокруг произвольного ромба (кроме квадрата) описать окружность нельзя.
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- If three angles of one triangle are equal to the corresponding angles of another triangle, then these triangles are:
- All isosceles triangles are:
- Every isosceles triangle is a:
- Each bisector of an isosceles triangle is its:
- Each bisector of an isosceles triangle is its:
- Every equilateral triangle is:
- Every equilateral triangle is:
- All equilateral triangles are:
- In a right-angled triangle, the hypotenuse is equal to the sum of the legs.
- All right-angled triangles are:
- The length of the hypotenuse of a right-angled triangle is less than the sum of the lengths of its legs.
- The area of a right-angled triangle is equal to the product of the lengths of its legs.
- The cosine of an acute angle of a right-angled triangle is equal to the ratio of the length of the adjacent leg to the length of the hypotenuse.
- The sum of the angles of a right-angled triangle is equal to 90 degrees.
- The sum of the acute angles of a right-angled triangle is equal to 90 degrees.
- The sum of the angles of an acute-angled triangle is 180°.
- The sum of the angles of an obtuse-angled triangle is 180°.
- A triangle with angles 30°, 75°, 75° is:
- The bisector of the vertex angle of an isosceles triangle, drawn to the base, divides the base into two equal parts.
- The bisector of the vertex angle of an isosceles triangle, drawn to the base, is perpendicular to the base.
- Any bisector of an equilateral triangle is its median.
- The median of an isosceles triangle, drawn from the vertex angle to the base, bisects this angle.
- The median of an isosceles triangle is its altitude.
- Any isosceles triangle has an axis of symmetry.
- Any isosceles triangle has a center of symmetry.
- Any equilateral triangle has a center of symmetry.
- Any equilateral triangle has three axes of symmetry.
- If one of the angles of a triangle is right, then the triangle is right-angled.
- If the hypotenuse and an acute angle of one right-angled triangle are respectively equal to the hypotenuse and an acute angle of another right-angled triangle, then these triangles are equal.
- If the two shorter sides of one right-angled triangle are equal to the two shorter sides of another right-angled triangle, then these triangles are similar.
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- The sum of the angles of a convex quadrilateral is 360 degrees.
- A circle can be inscribed in a quadrilateral.
