Geometry: I want to understand some points

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Homework Help Overview

The discussion revolves around a geometry problem involving the relationship between an arc of a great circle, its chord, and the radius of the circle. The original poster seeks to determine an unknown variable related to these elements.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants explore the geometric relationships between the arc, chord, and radius, with some attempting to express the radius in terms of the unknown variable. Questions arise regarding the meaning of "recedes from its chord" and the implications of this phrasing.

Discussion Status

There is an ongoing exploration of the problem with various interpretations being discussed. Some participants offer potential relationships and distances, while others seek clarification on terminology and concepts. No consensus has been reached, but several lines of reasoning are being examined.

Contextual Notes

Participants are working with specific geometric properties and relationships, including references to triangle properties and angles. The original poster has provided a figure for context, though its details are not described in the text.

irony of truth
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What is my unknown (say x) if I am finding the value in which an arc of a great circle 10 units long recedes from its chord? (given radius R and angle alpha?)

Here's my figure as an attachment...
 

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I am guessing, you can express R = xR + (1-x)R where (1-x)R is the height of your (isosceles) triangle and xR is the bit from the chord to the circle.
 
Last edited:
What do you mean by "recedes from its chord"?
 
HallsofIvy, seems like the arc is moving away from its respected chord (form by the two enddpoints of the arc)

My friend told me that x = R - R cos (alpha)... I wonder why...
 
He has given the greatest distance between the arc and the chord i.e. the difference of the radius and distance of the chord from the center
 
hi
By using the laws properties of triangle you will get the angle to be 45 degrees and
R to be square root of 50

http://www.mathsrevision.net/gcse/pages.php?page=47
 
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