- #1
karush
Gold Member
MHB
- 3,269
- 5
it was done by simple observationtypos maybe,,,,
Also, posted on MeWe and Linkedin
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In summary, the concept of "-3 circles centers on line segment PQ" means that there are three circles with their centers located on the line segment PQ. This can be visualized as three circles placed on a straight line segment with their centers lying on the line segment but not necessarily touching each other. The significance of this concept lies in its use in geometry to show the relationship between three circles with a common point of intersection on a line segment. The line segment PQ can be of any length as long as it can accommodate the centers of the three circles. This concept is also related to the intersecting chords theorem, which states that the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of
it was done by simple observationtypos maybe,,,,
Also, posted on MeWe and Linkedin
- #2
skeeter
- 1,103
- 1
One should not assume the two smaller diameters are equal ...
Large circle diameter, $D = PR+RQ$
$\pi D = \pi(PR+RQ) = \pi \cdot PR + \pi \cdot RQ$
Large circle diameter, $D = PR+RQ$
$\pi D = \pi(PR+RQ) = \pi \cdot PR + \pi \cdot RQ$
- #3
karush
Gold Member
MHB
- 3,269
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good point...
yes I know often the GRE diagrams are not for assumptions
so just adding as equal term is not absolute
yes I know often the GRE diagrams are not for assumptions
so just adding as equal term is not absolute
1. What does it mean for -3 circles to have centers on line segment PQ?
Having -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.
2. How is the position of the circles determined on line segment PQ?
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.
3. Is it possible to have -3 circles with centers on line segment PQ of different sizes?
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.
4. What is the significance of having -3 circles with centers on line segment PQ?
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.
5. How can the Apollonian circles with -3 centers on line segment PQ be applied in real life?
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.
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