document.write( "Question 485478: If a circle is inscribed in an equilateral triangle of side 2v3 units, then radius of the circle is \n" ); document.write( "

Algebra.Com's Answer #332066 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "In an equilateral triangle, the internal angle bisectors, \r\n" );
document.write( "the altitudes and the medians are all the same. The center\r\n" );
document.write( "of the inscribed circle is where the angle bisectors cross,\r\n" );
document.write( "so we draw an angle bisector to the center of the circle,\r\n" );
document.write( "and a radius from the center of the circle to the lower side\r\n" );
document.write( "of the triangle.  Since the internal angles of an equilateral\r\n" );
document.write( "triangle are 60°, the angle bisector of the angle divides it\r\n" );
document.write( "into two 30° angles. Since each side of the triangle is 2V3, the\r\n" );
document.write( "raidus divides the bottom side side into two parts each V3 in \r\n" );
document.write( "length.  I will label the radius r:\r\n" );
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document.write( "That is a 30°,60°,90° triangle so its hypotenuse is twice the\r\n" );
document.write( "shorter side,  So the hypotenuse is 2r and we have, by the\r\n" );
document.write( "Pythagorean theorem:\r\n" );
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document.write( "So the radius is 1.\r\n" );
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document.write( "Edwin

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