State whether each of the following statements is true or false:
$(1)$ The collection of all the points in a plane,which are at a fixed distance from a fixed point in the plane,is called a circle.
$(2)$ The line segment joining the centre and any point on the circle is called a radius of the circle.
$(1)$ The collection of all the points in a plane,which are at a fixed distance from a fixed point in the plane,is called a circle.
$(2)$ The line segment joining the centre and any point on the circle is called a radius of the circle.
(A) $(1)$ True. By definition,a circle is the set of all points in a plane that are at a fixed distance (the radius) from a fixed point (the centre).
$(2)$ True. By definition,the line segment connecting the centre of the circle to any point on its circumference is known as the radius.
$(2)$ True. By definition,the line segment connecting the centre of the circle to any point on its circumference is known as the radius.
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