Graduate Management Admission Test (GMAT) Practice Test

What defines a figure being inscribed within a circle?

1. All sides are equal

2. All vertices are on the circumference

3. The center point is inside the figure

4. All angles are right angles

The correct answer is: All vertices are on the circumference

A figure is defined as being inscribed within a circle when all of its vertices lie on the circumference of the circle. This means that every corner point of the figure touches the circle, and as a result, the circle is said to circumscribe the figure. This property is essential for various geometric calculations and concepts, particularly in relation to polygons and their interactions with circles. For example, with a polygon inscribed in a circle, one can derive important properties such as the relationship between the angles and the lengths of the sides. This is foundational in understanding shapes like triangles or quadrilaterals, where each vertex contributes to defining the overall geometric characteristics in relation to the circle. The other attributes listed do not define inscribed figures. For instance, equal sides or angles being right angles pertain to specific types of polygons (like equilateral triangles or squares) but do not indicate whether the figure is inscribed. Additionally, having the center point inside the figure describes the relationship of the figure to the circle in a more general way, not specifically addressing the criteria for being inscribed.