Question

Natasha drew two arcs of the same radius by placing her compass at each endpoint of ab to produce the picture below. What is the shape formed by the two arcs?

1) Circle
2) Triangle
3) Rectangle
4) Square

Answer 1

The shape formed by two arcs of the same radius drawn from each endpoint of a line segment is a circle.

Step-by-step explanation:

The shape formed by two arcs of the same radius drawn from each endpoint of line segment AB is a circle. When you open a compass to the length of the radius and draw an arc from each endpoint of a line segment without changing the compass' width, the arcs will intersect at points which are equidistant from both endpoints of the line segment. This describes the process of constructing the circumcircle of a triangle formed by the two endpoints and any point on the arc. Since a circle is defined as a set of points that are equidistant from a center point, these constructions create partial circles, but if extended would form a complete circle.