document.write( "Question 385197: A central angle intercepts an arc of a circle equal in length to a diameter of the circle, find the measure of the central triangle in radians. \n" ); document.write( "

Algebra.Com's Answer #272570 by Edwin McCravy(20055) $\"\"$ $\"About$

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A central angle intercepts an arc of a circle equal in length to a diameter of
\n" ); document.write( "the circle, find the measure of the central angle in radians.
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document.write( "By definition, a central angle which intercepts an arc of a circle equal in\r\n" );
document.write( "length to a radius has a measure of 1 radian.\r\n" );
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document.write( "Since a diameter is twice a radius, a central angle intercepts an arc of a\r\n" );
document.write( "circle equal in length to a diameter of the circle has a measure of two\r\n" );
document.write( "radians.\r\n" );
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document.write( "The picture on the left below is a central angle which intercepts an arc of the\r\n" );
document.write( "circle equal in length to a radius and thus has a measure of 1 radian.\r\n" );
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document.write( "The picture on the right below is your problem. It is a central angle which\r\n" );
document.write( "intercepts an arc of a circle equal in length to a diameter and thus has a\r\n" );
document.write( "measure of 2 radians. \r\n" );
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document.write( "The green arc on the left is equal in length to 1 radius, and measures 1 radian.\r\n" );
document.write( "The green arc on the right is equal in length to 1 diameter, or 2 radii, and\r\n" );
document.write( "therefore measures 2 radians.\r\n" );
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document.write( "Edwin

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