document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197946>Question 1197946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is a circle of diameter 24 cm. It is folded along vertical chord AB so that point D on the circumference coincides with the centre C. The area of the shaded region, in cm^2 is:<BR>\n" );
document.write( "a) 192π - 72√3<BR>\n" );
document.write( "b) 24π - 18√3<BR>\n" );
document.write( "c) 48π - 18√3<BR>\n" );
document.write( "d) 192π - 144√3<BR>\n" );
document.write( "e) 48π - 36√3\r<BR>\n" );
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document.write( "I have tried to draw out some angles and such to find ratios to no avail. </SPAN>\n" );
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document.write( "Nice problem -- except we don't know what the shaded region is.<br><BR>\n" );
document.write( "The diagram below should help YOU find your answer, since YOU know what the shaded region is.<br><BR>\n" );
document.write( "The problem says a given circle with diameter 24 (radius 12) is folded along a vertical chord so that the point D on the circumference of the circle coincides with the center C of the circle.  We can picture that by drawing a second circle with radius 12 centered at D.<br><BR>\n" );
document.write( "The picture of the two circles before circle C is folded along vertical chord AB then looks like this:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28800%2C600%2C-15%2C25%2C-15%2C15%2Ccircle%280%2C0%2C12%29%2Ccircle%2812%2C0%2C12%29%0D%0A%2Cline%286%2C-6sqrt%283%29%2C6%2C6sqrt%283%29%29%2Cline%280%2C0%2C6%2C6sqrt%283%29%29%2Cline%2812%2C0%2C6%2C6sqrt%283%29%29%2Cline%280%2C0%2C6%2C-6sqrt%283%29%29%2Cline%2812%2C0%2C6%2C-6sqrt%283%29%29%2Cline%280%2C0%2C12%2C0%29%0D%0A%2Clocate%286%2C-12%2CB%29%2Clocate%286%2C12%2CA%29%2Clocate%28-1%2C0%2CC%29%2Clocate%2813%2C0%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You should be able to calculate the area of any region of the figure using these....<br><BR>\n" );
document.write( "Each of the equilateral triangles ACD and BCD has an area of (side squared times sqrt(3))/4 = 36*sqrt(3).<br><BR>\n" );
document.write( "Each of the four 30-60-90 triangles formed by the chord AB and the two equilateral triangles has an area of half the area of each equilateral triangle: 18*sqrt(3).<br><BR>\n" );
document.write( "Each of the four segments of a circle CAD, CBD, DCA, and DCB has an area one-sixth of the area of each circle: (144pi)/6 = 24pi.<br><BR>\n" );
document.write( "Each of the four regions between a side of one of the equilateral triangles and one of the circles has an area (circular segment of circle, minus equilateral triangle) of 24pi-36*sqrt(3).<br><BR>\n" );
document.write( "It seems the most likely shaded region in your problem is the area of the folded-over portion of circle C; in that case, using the work shown you should get answer choice e.<br><BR>\n" );
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