Question

Draw different pairs of circles. How many points does each pair have in common?
What is the maximum number of points in common?

Answer 1

Hint:
Draw different pairs of circles in different ways. A common point is such a point which lies on both the curves more precisely both circles. If we have an equation of both circles then a common point will satisfy both the equations simultaneously.

Complete step by step solution:
A)

Above pair of circles have no point in common. That is, the number of common points is 0.

B)

Above pair of circles have only one point in common. That is, the number of common point is 1.

C)

Above pair has two points in common. That is, the number of common points is 2.
And this is the maximum number of common points you can draw.

Note:
1) A circle is defined as a set of all points that are equidistant from a common point.
2) This common point is called the center of the circle.
3) That equal distance is called radius of circle.
4) Line joining any two points on a circle is called a chord.
5) A circle has a number of chords.
6) Diameter is the largest chord of the circle because it passes through the center of the circle.
7) A pair of circles having a center in common are called circumcircles.
8) Diameter of the circle is two times the radius of the circle.