Geometry: I want to understand some points

In summary, the conversation discusses finding the unknown value (x) when given the length of an arc and other variables such as the radius (R) and angle (alpha). The figure attached shows a triangle and the formula R = xR + (1-x)R is suggested to find the unknown value. The term "recedes from its chord" refers to the arc moving away from the chord. The friend suggests using x = R - R cos (alpha) to find the value and explains that it represents the greatest distance between the arc and chord. The conversation also mentions using the properties of a triangle to find the angle and radius.
  • #1
irony of truth
90
0
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...
 

Attachments

  • s the figure.JPG
    s the figure.JPG
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  • #2
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.
 
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  • #3
What do you mean by "recedes from its chord"?
 
  • #4
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...
 
  • #5
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
 
  • #6
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
 
Last edited by a moderator:

What is geometry?

Geometry is a branch of mathematics that focuses on the study of shapes, sizes, and positions of objects in space.

What are the basic elements of geometry?

The basic elements of geometry include points, lines, and angles. Points are represented by a dot and have no size or dimension. Lines are straight and extend infinitely in both directions. Angles are formed by two intersecting lines or line segments.

What is the difference between 2D and 3D geometry?

2D geometry deals with shapes and figures that are flat and have only two dimensions - length and width. 3D geometry, on the other hand, involves objects that have three dimensions - length, width, and depth.

What are some applications of geometry in real life?

Geometry has many practical applications in our daily lives, such as in architecture, engineering, navigation, art, and design. It is also used in fields like astronomy, physics, and computer graphics.

How can I improve my understanding of geometry?

To understand geometry better, you can start by studying the basic concepts and principles, practicing with different problems, and visualizing shapes and figures in your mind. You can also use online resources, textbooks, or seek help from a tutor or teacher.

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