document.write( "Question 631112: In circle A, the sector PAC is to be filled with blue flowers while the rest of the bed shown in the figure is to be yellow. If radius PA = 8 ft and measure angle PAC = 30 , what is the measure of arc PC ?
\n" ); document.write( "(1)3/4 pi
\n" ); document.write( "(2)4/3 pi
\n" ); document.write( "(3)30 degrees
\n" ); document.write( "(4)42 degrees \n" ); document.write( "

Algebra.Com's Answer #397371 by jsmallt9(3758) $\"\"$ $\"About$

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The name of a circle is the name of its center. So the center of circle A is the point A. This makes angle PAC a central angle. This is important because we will be using the following proportion which connects central angles and the their related arcs:
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\r\n" );
document.write( "           \r\n" );
document.write( "part       Central Angle      length of arc\r\n" );
document.write( "-----  =   -------------  =  ----------------\r\n" );
document.write( "whole          360                 \r\n" );
document.write( "

\n" ); document.write( "Putting the given angle and radius we get:
\n" ); document.write( " $\"30%2F360+=+x%2F%282pi%2A8%29\"$
\n" ); document.write( "The left side reduces to:
\n" ); document.write( " $\"1%2F12+=+x%2F%282pi%2A8%29\"$
\n" ); document.write( "Cross-multiplying we get:
\n" ); document.write( " $\"12x+=+16pi\"$
\n" ); document.write( "Dividing by 12:
\n" ); document.write( " $\"x+=+16pi%2F12\"$
\n" ); document.write( "which reduces to:
\n" ); document.write( " $\"x+=+4pi%2F3\"$
\n" ); document.write( "or
\n" ); document.write( " $\"x+=+%284%2F3%29pi\"$ \n" ); document.write( "

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