document.write( "Question 1066307: Three circles of radius 2 cm overlap so that each passes through the centre of the other 2. The area of centre section is? \n" ); document.write( "

Algebra.Com's Answer #681497 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "Three circles of radius 2 cm overlap so that each passes through the centre of the other 2. The area of centre section is?
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\n" ); document.write( "\n" ); document.write( "Let me re-formulate the question:\r
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document.write( "      Find the area of the common part of the three circles.\r\n" );
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document.write( "1.  Make a sketch. Let the points A, B and C are the centers of these circles.\r\n" );
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document.write( "    Connect the centers by straight line segments.\r\n" );
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document.write( "    You will get the equilateral triangle. \r\n" );
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document.write( "    Why it is equilateral ?? - Because it has three sides of equal length.\r\n" );
document.write( "                               The length of each side is equal to the radius, namely, 2 cm.\r\n" );
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document.write( "2.  Now, what is this common area of these three circles?\r\n" );
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document.write( "    It is THIS equilateral triangle PLUS three segments of the circles.\r\n" );
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document.write( "    On \"segments of the circles\" see the lesson\r\n" );
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document.write( "        Area of a segment of the circle \r\n" );
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document.write( "    in this site.\r\n" );
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document.write( "3.  The area of each segment of the circle is equal to the area of the sector minus the area of the triangle.\r\n" );
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document.write( "    Our segments of the circles are special: they are 60 degrees.\r\n" );
document.write( "    So, the area of each of the three segments is  of the area of the circle minus the area of the equilateral triangle with the side of 2 cm.\r\n" );
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document.write( "4.  Now I suppose, that after getting full, clear and comprehensive explanations you are able to complete the solution on your own.\r\n" );
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document.write( "If you still have difficulties in this way, let me know by sending me your message through the \"Thank you\" window/section/table/form.\r\n" );
document.write( "If you do, do not forget to include the ID number of this problem (# 1066307) in order for I could identify it.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Regarding the areas of different figures we considered on the way, see this free of charge online textbook \r
\n" ); document.write( "\n" ); document.write( " GEOMETRY - YOUR ONLINE TEXTBOOK \r
\n" ); document.write( "\n" ); document.write( "especially its chapter \"Area of a circle, of a sector and of a segment of a circle.\r
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