Arc length and chord distance for a great circle

[irony of truth]

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...

 

[EnumaElish]

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.

 

[HallsofIvy]

What do you mean by "recedes from its chord"?

 

[irony of truth]

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...

 

[mukundpa]

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

 

[gopi krishna]

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