Question

Доведіть, що коли навколо ромба можна описати коло, то цей ромб є квадратом

Answer 1

Если сумма противоположных углов равна 180, то вокруг него можно описать окружность. Не около каждого роста можно описать, он будет квадратом, потому, что каждый угол равен 90 , а сумма его противоположных 180

Answer 2

Checking the Conditions for a Rhombus to be a Square

To prove that a rhombus is a square when a circle can be circumscribed around it, we need to consider the properties of both shapes.

Rhombus: A rhombus is a quadrilateral with all four sides of equal length. It is also a type of parallelogram, which means its opposite sides are parallel and equal in length.

Square: A square is a special type of rhombus where all angles are right angles (90 degrees).

Relationship Between a Rhombus and a Circle

When a circle can be circumscribed around a rhombus, it means that the vertices of the rhombus lie on the circumference of the circle. This implies that the distance from the center of the circle to each vertex of the rhombus is the same, which is the radius of the circle.

Conclusion

Given that a circle can be circumscribed around a rhombus, it follows that the rhombus is equidistant from the center of the circle at all its vertices. This implies that the diagonals of the rhombus are equal and intersect at right angles, making it a square.

Therefore, when a circle can be circumscribed around a rhombus, the rhombus is indeed a square.