document.write( "Question 1199742: The circle with center O is inscribed in kite ABCD. Find the length of the radius of the circle, in cm.\r
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\n" ); document.write( "\n" ); document.write( "A) 9 $\"+3%2F5+\"$
\n" ); document.write( "B) 8 $\"+5%2F11+\"$
\n" ); document.write( "C) 11 $\"+1%2F3+\"$
\n" ); document.write( "D) 10 $\"+2%2F7+\"$
\n" ); document.write( "E) 12 $\"+5%2F13+\"$ \n" ); document.write( "

Algebra.Com's Answer #833707 by ikleyn(52799) $\"\"$ $\"About$

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\n" ); document.write( "The circle with center O is inscribed in kite ABCD. Find the length of the radius of the circle, in cm.
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document.write( "The area of the right-angled triangle ABC is half the product of its legs   cm^2.\r\n" );
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document.write( "The area of the right-angled triangle ADC is the same  cm^2.\r\n" );
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document.write( "So, the area of the kit is simply  24*18  cm^2.\r\n" );
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document.write( "    For any convex polygon circumscribed around a circle, \r\n" );
document.write( "    its area is half the product the radius of the circle \r\n" );
document.write( "    by the perimeter of the polygon\r\n" );
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document.write( "        area of the polygon = .\r\n" );
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document.write( "In our case, the perimeter of the kite is 2*(24+18) = 2*42 = 84 cm.\r\n" );
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document.write( "So we have\r\n" );
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document.write( "    area of the kite = 24*18 =  = 42r,\r\n" );
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document.write( "which gives  r =  =  =  = 10  cm.    ANSWER\r\n" );
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