If the circle is inside the square, four.
8
The two points and the centre of the earth define a plane, and the intersection of this plane with the surface of the earth is a circle - the "Great Circle". The shortest distance between the two points is the smaller of the two arcs on this circle.
The solution set is all points on the circle.
a circle?
One
6 maximum points of intersection
10.
8
discuss the possible number of points of interscetion of two distinct circle
Six (6)
12
69
32
The greatest number of intersection points with just four lines is 6.
Yes. Draw three line segments so that they cross at three points forming a triangle (with each side extending beyond the vertices of the triangle). Draw one circle to enclose the triangle without touching it to intersect the extended sides at a further 6 points, making 9 points of intersection so far. Draw the second circle slightly shifted (relative to the first) so that it also encloses the triangle (without touching it) creating a further 6 intersection points with the three lines and 2 with the first circle; an additional 8 intersection points making 17 in all.
There are an infinite number of points on the circumference of a circle and an infinite number of points on a semi-circle so the answer to your question is "An infinite number of pairs of points."
The great circle is the intersection of a sphere and any plane passing through its centre. Given two distinct points on the surface of a sphere, those two points and the centre of the sphere define a plane. [If one of the points is at the antipodes of the other, an infinite number of planes are defined.] The great circle is the circle formed when that plane meets the surface of the sphere.