document.write( "Question 1189064: If a sphere has a radius of 6cm rests on 3 horizontal wires forming a plane triangle whose sides are 5cm, 12cm, and 13cm. Find the height of the top of the sphere above the plane of the wires.
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Algebra.Com's Answer #820283 by ikleyn(52943) $\"\"$ $\"About$

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\n" ); document.write( "If a sphere has a radius of 6cm rests on 3 horizontal wires forming a plane triangle
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document.write( "The plane of triangle cuts the sphere, and the section is the circle inscribed in the triangle.\r\n" );
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document.write( "For any triangle, the radius of the inscribed circle is the area of the triangle divided by its semi-perimeter\r\n" );
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document.write( "    r = .\r\n" );
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document.write( "In our case, the triangle is right-angled (the triple 5,12,13 is the Pythagorean triple), \r\n" );
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document.write( "so its area is half the product of its legs S =  = 30 cm^2.\r\n" );
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document.write( "The perimeter of the triangle is  P = 5 + 12 + 13 = 30 cm.\r\n" );
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document.write( "So, the radius of the inscribed circle is r =  = 2 cm.\r\n" );
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document.write( "Hence, the distance from the center of the sphere to the cutting plane is   =  =  =  cm.\r\n" );
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document.write( "The top of the sphere above the cutting plane is  6 +  = 11.657 cm (rounded).    ANSWER\r\n" );
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