Proving Shortest Distance Between 3 Points on a Circle

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SUMMARY

The discussion focuses on proving that the shortest distance between any two points on the perimeter of a circle is always less than or equal to the distance between the other point and either of the two points. The participants clarify that the distance in question refers to the segments connecting the three points on the circle's circumference. The maximum distance between any two points is defined as the diameter (D) of the circle, with the distance ranging from 0 to D.

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  • Understanding of basic geometry concepts, particularly circles.
  • Familiarity with the properties of diameters and circumferences.
  • Knowledge of distance measurement along a circular path.
  • Ability to interpret geometric diagrams and illustrations.
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  • Research the properties of circles, focusing on the relationship between points on a circumference.
  • Study geometric proofs related to distances on circular paths.
  • Explore the concept of arc lengths and their calculations.
  • Learn about the application of the triangle inequality theorem in circular geometry.
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Mathematicians, geometry students, and educators looking to deepen their understanding of circular geometry and distance relationships between points on a circle.

roni1
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I have 3 point on a perimeter of circle.
How I prove/show between every the two point of them there is always short way that the way between the other points?
 
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Re: question

roni said:
I have 3 point on a perimeter of circle.
How I prove/show between every the two point of them there is always short way that the way between the other points?

Are you talking about the distance along the circumference of the circle?
 
Re: question

I mean to segments between the 3 points.
 
Re: question

roni said:
I mean to segments between the 3 points.

Can you provide a diagram illustrating what you're trying to do?
 
Re: question

The answer:
The distance be between 0 to D.
D = diameter.
Am I right?
 
Re: question

roni said:
The answer:
The distance be between 0 to D.
D = diameter.
Am I right?
As it seems that we don't know what the question is asking I don't think anyone can tell you if that's right or not.

-Dan
 

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