Consider a circle with radius 5 and another circle with radius 3. Let d represent the distance between the two centers.We want to know how many intersections there are of these two circles for different values of d.Draw figure id d=10?

Answer:If d<2, there is no intersectionIf d=2, there is one intersectionIf 2<d<8, there are two intersectionsIf d=8, there is one intersectionif d>8, there is no intersectionStep-by-step explanation:If d<2 (the difference between both radius is 2), the little circle is inside the big one. Thus there is no intersection.If d=2, the little circle is inside but tangent to the big one. There is one intersection then.If 2<d<8, there are two intersections since the little circle has a portion outside the big one, and another portion inside.If d=8, the little circle is tangent to the big one from outside. There is one intersection then.if d>8, the little circle is completely exterior to the big one. Thus, there is no intersection.Please find attached the figure for d = 10. The big circle is centered and the other is offset by 10.