I have two eclipsing circles that are both 70 inches in diameter. I need the excel formulas to determine the area of the eclipse and when I have a chord length of x then what is the circumference of that portion of the circle.
The formulas that I have currently are as follows based upon the following information. G9 = Radius = 35, F9 = Diameter = 70, C15 = Chord = 30.
1) I am attempting to find the center of the inside circle to the middle of the intersect of the outside circle. The formula I have is =SQRT((G9)*(G9)-(C15/2)*(C15/2)) With this formula the answer I got was 31.623
2) Surface Area Reduction of Inner Circle When Eclipsed by Outer Circle. (Basically the loss of area assuming one circles area stays intact. Formula I have is; =SUM(pi)x((G9-E15)+(C15/2)*(C15/2)*2 In this example E15 = 31.623 which is also from the first formula, cell (I6). The answer to this formula for the surface area that I got is 1485.38
3) Arc of the circle when the chord is 30. I had to do this in two formulas but I'm sure there is a way to do this in one.
1st Formula =ASIN((C15/2)/(G9) = .443 = I6 (cell)
2nd Formula =DEGREES((16)*(F9*(pi)/180) The answer that I got for this formula was 31.0038
What's important of course is what I'm trying to achieve is actually the right way of expressing it, in other words the formula mathematically may be right but does the result reflect what I am trying to achieve.
If anyone can provide assistance it would be greatly appreciated.
The formulas that I have currently are as follows based upon the following information. G9 = Radius = 35, F9 = Diameter = 70, C15 = Chord = 30.
1) I am attempting to find the center of the inside circle to the middle of the intersect of the outside circle. The formula I have is =SQRT((G9)*(G9)-(C15/2)*(C15/2)) With this formula the answer I got was 31.623
2) Surface Area Reduction of Inner Circle When Eclipsed by Outer Circle. (Basically the loss of area assuming one circles area stays intact. Formula I have is; =SUM(pi)x((G9-E15)+(C15/2)*(C15/2)*2 In this example E15 = 31.623 which is also from the first formula, cell (I6). The answer to this formula for the surface area that I got is 1485.38
3) Arc of the circle when the chord is 30. I had to do this in two formulas but I'm sure there is a way to do this in one.
1st Formula =ASIN((C15/2)/(G9) = .443 = I6 (cell)
2nd Formula =DEGREES((16)*(F9*(pi)/180) The answer that I got for this formula was 31.0038
What's important of course is what I'm trying to achieve is actually the right way of expressing it, in other words the formula mathematically may be right but does the result reflect what I am trying to achieve.
If anyone can provide assistance it would be greatly appreciated.