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February 23rd, 2011, 04:45 AM  #1 
Member Joined: Nov 2010 Posts: 53 Thanks: 0  Could anyone help me with this figure?
I am working with one of Hippocrats famous moons. There is one part of the geometry I don`t get, see figure! I know that but how de we know this? (a_1 = Area defined by AC and the circle a_2 = Area defined by BC and the circle A = Area defined by the line AB and a circle with radius AD and center in D) 
February 23rd, 2011, 05:31 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Could anyone help me with this figure?
[attachment=0:3rdvgl6b]lunes.PNG[/attachment:3rdvgl6b] The radius DB is times the length of the radius OB. Therefore the circle centred at D has twice the area as the circle centred at O. But if you tilt the diagram 45°, you can see that circular segment labelled A is similar to the segments a1 and a2, so its proportions must vary similarly. Thus A must also have twice the area as either of a1 or a2. 
February 23rd, 2011, 07:23 AM  #3 
Member Joined: Nov 2010 Posts: 53 Thanks: 0  Re: Could anyone help me with this figure?
Ah, I see. Thank you.


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