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You can put this solution on YOUR website!
the lengths of two parallel chords in a circle.
\n" ); document.write( "The lengths are 16 and 30.
\n" ); document.write( "The distance between these chords is 23.
\n" ); document.write( " How can I find the radius of this circle?
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\n" ); document.write( "This will be easily understood if you roughly draw this out. We don't need to
\n" ); document.write( "draw a circle. We will solve this using right triangles
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\n" ); document.write( "This is the way I pictured it
\n" ); document.write( "Draw the chords horizontally, the shorter (16) one above the longer one
\n" ); document.write( "Join the half way points of the chords, this line is 23 units, the center will fall on this line.
\n" ); document.write( "Mark the center closer to the longer chord
\n" ); document.write( "The radii run from the center to the ends of each chord and form the the hypotenuse of the right triangles.
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\n" ); document.write( "We will find the distance each chord is from the center.
\n" ); document.write( "let x = distance from the longer chord to the center
\n" ); document.write( "then
\n" ); document.write( "(23-x) = distance from the shorter chord to the center
\n" ); document.write( "let r = the radius and will be the hypotenuse of the triangles
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\n" ); document.write( "Two pythag equations
\n" ); document.write( ":
\n" ); document.write( "Short chord triangle
\n" ); document.write( "8^2 + (23-x)^2 = r^2
\n" ); document.write( "64 + 529 - 46x + x^2 = r^2
\n" ); document.write( "593 - 46x + x^2 = r^2
\n" ); document.write( "and
\n" ); document.write( "Long chord triangle
\n" ); document.write( "15^2 + x^2 = r^2
\n" ); document.write( "225 + x^2 = r^2
\n" ); document.write( ":
\n" ); document.write( "Since they both = r^2, we can write it
\n" ); document.write( "225 + x^2 = 593 - 46x + x^2
\n" ); document.write( "Subtract x^2 from both sides, solve for x
\n" ); document.write( "46x = 593 - 225
\n" ); document.write( "46x = 368
\n" ); document.write( "x =
\n" ); document.write( "x = 8, is the distance the longer chord is from the center
\n" ); document.write( "and
\n" ); document.write( "23-8 = 15, is the distance the shorter chord is from the center
\n" ); document.write( ":
\n" ); document.write( "Solve for r (hypotenuse) of one of the equation
\n" ); document.write( "r^2 = 8^2 + 15^2
\n" ); document.write( "r^2 = 64 + 225
\n" ); document.write( "r^2 = 289
\n" ); document.write( "r =
\n" ); document.write( "r = 17 is the radius of the circle
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\n" ); document.write( "note that r will be the same from either triangle.
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\n" ); document.write( ":
\n" ); document.write( "I tried to explain this so it would make sense to you.
\n" ); document.write( "I would appreciate it, if you would let me know, if I succeeded. C \n" ); document.write( "