Nathan drew an 8-centimeter line segment. With one of the endpoints of the line segment as the center, he then drew a circle with a radius of 3 centimeters. How many triangles can he create that have the 8-centimeter line segment as one side and a radius of the circle as another side?"
A.
only one triangle
B.
infinitely many triangles
C.
eight triangles
D.
four triangles
To create a triangle with the 8-centimeter line segment as one side and a radius of the circle as another side, the third side of the triangle must be longer than the difference between the radius of the circle and the length of the line segment (i.e. 3 cm - 8 cm = -5 cm, which is not possible since lengths cannot be negative). Therefore, Nathan cannot create any triangles with the given conditions. The answer is A. only one triangle.
