it was done by simple observationHaving -3 circles with centers on line segment PQ means that there are three circles that are positioned in such a way that their centers all lie on the same line segment PQ. This can also be interpreted as the circles being tangent to each other.
The position of the circles on line segment PQ is determined by the distance between the centers of the circles and the length of line segment PQ. The closer the centers of the circles are to each other, the smaller the circles will be in size.
Yes, it is possible to have -3 circles with centers on line segment PQ of different sizes. This can happen when the distance between the centers of the circles is not equal or when the length of line segment PQ is not the same for all three circles.
The significance of having -3 circles with centers on line segment PQ is that it represents a special geometric configuration. This configuration is known as the Apollonian circles and it has been studied extensively in mathematics and physics.
The Apollonian circles with -3 centers on line segment PQ have various applications in different fields such as optics, crystallography, and even art. They can also be used to model the behavior of light in certain situations and in the design of optical devices.