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Just to finish it off:
Yes, sorry. I edited it.
Don't you mean 108?
Okay. If you leave the surds as is without simplification you will also get the exact answer of 108.
Ah, I get it. Great! Do you use SketchPad to get the area?
Hm, how did you get the second to last row?
Using R = 12 + r this becomes
Eliminate alpha by adding
Okay. Post when you get the equations.
Thanks. Working on that now.
ABD with the angle alpha and ABC with angle 180-alpha.
Well, I just noticed that the point where the circles touch is on the same line as A and B (because they are the centers of the two circles), and got from that that R=AB+r, that is, AC=AB+BD. Now we can use the Cosine Rule to get,
where alpha is the acute angle of the rhombus. We can get from that equation the cosine of the angle and thus also its sine. We then use the formula for calculating the area of parallelogram using its sides and internal angle.
It might help Bob to know what the correct answer is. I think once he gets the sides to 12 he will get it.