Geometry: I want to understand some points

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...



Science Advisor
Homework Helper
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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Science Advisor
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....


Homework Helper
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

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