document.write( "Question 1034430: Two parallel chords, one 10 and the other 16 and 13 units apart. Find the diameter. \n" ); document.write( "

Algebra.Com's Answer #649070 by ikleyn(52906) $\"\"$ $\"About$

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\n" ); document.write( "Two parallel chords, one 10 and the other 16 and 13 units apart. Find the diameter.
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document.write( "Unclear.\r\n" );
document.write( "Read your post.\r\n" );
document.write( "How many chords?\r\n" );
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\n" ); document.write( "Comment from student: The first thing I said was two chords, there 2 on opposite sides of the circle.
\n" ); document.write( "The one closer to the top is 10 units and the bottom chord is 16. The chords are 13 units apart.
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\n" ); document.write( "\n" ); document.write( "My response:\r
\n" ); document.write( "\n" ); document.write( "First formulation was BAD. The second makes things clearer, although is not perfect.
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document.write( "Please make a sketch.  Draw the diameter parallel to the chords.\r\n" );
document.write( "There are TWO possible configurations. \r\n" );
document.write( "1) The chords are in one side of the diameter.\r\n" );
document.write( "2) The chords are in different sides.\r\n" );
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document.write( "I will consider here only the configuration #1, leaving #2 to you.\r\n" );
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document.write( "Let \"x\" be the distance from the center to the first chord and \"y\" be the distance from the center to the first chord.\r\n" );
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document.write( "Then you have this system of 3 equations \r\n" );
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document.write( "x + y = 13,          (1)     (in configuration #2 it is   x - y = 13)\r\n" );
document.write( " = ,      (2)\r\n" );
document.write( " = .      (3)\r\n" );
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document.write( "Here 5 in (2) is half of 10, while 8 in (3) is half of 16.\r\n" );
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document.write( "Distract equation (3) from (2)  (both sides). You will get\r\n" );
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document.write( " = ,  or\r\n" );
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document.write( "(x+y)*(x-y) = 64 - 25,  or\r\n" );
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document.write( "(x+y)*(x-y) = 39.     (4)\r\n" );
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document.write( "In (4), replace x+y by 13 due to (1). You will get\r\n" );
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document.write( "x - y =  = 3.\r\n" );
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document.write( "Now you have two equations:\r\n" );
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document.write( "x + y = 13.      ( it is former equation (1) )\r\n" );
document.write( "x - y =  3.\r\n" );
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document.write( "Add them to get 2x = 16 and x = 8.\r\n" );
document.write( "Then y = 5.\r\n" );
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document.write( "The problem is solved (in half, i.e. for configuration #1).\r\n" );
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document.write( "For #2 please do it yourself following the same scheme.\r\n" );
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