Question

in a circle with center a and radius ab, let p be a point of ab that is not an endpoint. explain whether or not p is on the circle. choose the correct answer. a. yes. every line segment drawn through the center of a circle will intersect the circle at two points. b. no, the endpoints of the line segment ab lie on the circle and it is not possible to draw a line segment which intersects the circle in three places. c. no because if the radius is ab, then one endpoint of ab lies on the circle. since p is not the endpoint, it cannot be on the circle. d. yes because if the radius is ab then one endpoint of ab is the center and does not lie on the circle. since p is not an endpoint, it can be on the circle.

Explanation:

The radius of a circle is a line - segment from the center of the circle to a point on the circle. Here, the radius is \(AB\) with \(A\) as the center. So, \(B\) lies on the circle. Since \(P\) is a non - endpoint of \(AB\), it is either between \(A\) (the center) and \(B\) (a point on the circle) and thus inside the circle, not on it.

Answer:

C. No because if the radius is \(AB\), then one endpoint of \(AB\) lies on the circle. Since \(P\) is not the endpoint, it cannot be on the circle.