Question

Укажіть неправильне твердження. А два вписаних кути, що спираються на одну дугу, є рівними. Б Якщо всі сторони чотирикутника дотикаються до кола, то чотирикутник с описаним. В Якщо коло лежить поза чотирикутником, то чотирикутник Є вписаним. Г Будь-який ромб можна описати навколо кола.​

Answer 1

Incorrect Statement:

The incorrect statement is: "If all sides of a quadrilateral touch a circle, then the quadrilateral is circumscribed."

Explanation:

Let's analyze each statement to determine which one is incorrect.

A. Two inscribed angles that intercept the same arc are congruent. This statement is correct. According to the inscribed angle theorem, if two angles are inscribed in a circle and intercept the same arc, then the angles are congruent. [[1]]

B. If all sides of a quadrilateral touch a circle, then the quadrilateral is circumscribed. This statement is incorrect. A quadrilateral is circumscribed around a circle if and only if its vertices lie on the circle. In other words, the circle passes through all four vertices of the quadrilateral. If all sides of a quadrilateral touch a circle, it is called a tangential quadrilateral, not a circumscribed quadrilateral. [[2]]

C. If a circle lies outside a quadrilateral, then the quadrilateral is inscribed. This statement is incorrect. A quadrilateral is inscribed in a circle if and only if its vertices lie on the circle. In other words, the circle passes through all four vertices of the quadrilateral. If a circle lies outside a quadrilateral, it does not necessarily mean that the quadrilateral is inscribed. [[3]]

D. Any rhombus can be circumscribed around a circle. This statement is correct. Any rhombus can be circumscribed around a circle. The center of the circle lies at the intersection of the diagonals of the rhombus, and the circle passes through all four vertices of the rhombus. [[4]]

In summary, the incorrect statement is: "If all sides of a quadrilateral touch a circle, then the quadrilateral is circumscribed."