I need to create a formula for excel that will solve the problem depicted in the drawing. Any help is appreciated.

http://www.smugmug.com/photos/697613115_NMf4q-XL.jpg

Printable View

- Oct 30th 2009, 01:42 PMT6902wsNeed help creating a formula
I need to create a formula for excel that will solve the problem depicted in the drawing. Any help is appreciated.

http://www.smugmug.com/photos/697613115_NMf4q-XL.jpg - Oct 30th 2009, 01:52 PMearboth
- Oct 30th 2009, 01:58 PMT6902ws
I understand the logic, I would like to see the open office formula.

- Oct 30th 2009, 02:22 PMearboth
I've attached a screen-shot of the spreadsheet:

R1 := radius of the outer circle

R2 := radius of the inner circle

d := length of the secant (with your example 30)

The formula is shown in the input line. Translate the word wurzel by sqrt (Wurzel is the German word for root)

I hope that this helps! - Oct 30th 2009, 09:08 PMukorov
according to the attached pic:

x + y = 30

y = 30 - x .....(1)

By Pythagarus Theorem.:

33^2 - (x + y)^2 = z^2

30^2 - y^2 = z^2

Hence

33^2 - (x + y)^2 = 30^2 - y^2

33^2 - 30^2 = (x + y)^2 - y^2

189 = x^2 + 2xy + y^2 - y^2

x^2 + 2xy = 189 .....(2)

(1) to (2), hence:

x^2 + 2x(30 - x) = 189

x^2 + 60x - 2x^2 - 189 = 0

-x^2 + 60x - 189 = 0

x^2 - 60x + 189 = 0

x = [-(-60) +/- (60^2 - 4 x 1 x 189)^0.5] / (2 x 1)

x = 56.66 (rejected)

or

x = 3.34 - Oct 31st 2009, 03:27 AMearboth
- Oct 31st 2009, 09:51 AMukorov
alright i am now aware of the problem. however x is not the difference of the two green lines either, because the question has never given that x + y is precisely equivalent to the length of the inner radius (30).

To ignore this arguement, we only use the Pyth. Th. twice:

(x + y)^2 + 15^2 = 33^2

(x + y)^2 = 33^2 - 15^2

x^2 + 2xy + y^2 = 864 .....(1)

y^2 + 15^2 = 30^2

y^2 = 675

y = (5)(27^0.5) .....(2)

(2) to (1) we have:

x^2 + 2x(5)(27^0.5) + 675 = 864

x^2 + (10)(27^0.5)x - 189 = 0

x = [-(10)(27^0.5) +/- (2700 + 4 x 189)^0.5] / 2

**x = 3.41**

or

x = -55.4 (rejected) - Nov 2nd 2009, 08:40 AMT6902ws
The correct answer is 3.41.

Thanks