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document.write( "
We draw in radii to \r\n" );
document.write( "the x-axis and to the ends of the chord\r\n" );
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document.write( "
\r\n" );
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document.write( "Since the circle is tangent to the x-axis at (4,0), the y-coordinate \r\n" );
document.write( "of the center is the same as the radius, r, so it's coordinates are\r\n" );
document.write( "(4,r) \r\n" );
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document.write( "The triangle formed with the chord is isosceles since its two legs are\r\n" );
document.write( "congruent radii. So we draw a median, in green, which is also an altitude, \r\n" );
document.write( "a vertex angle bisector, and a perpendicular bisector which divides the \r\n" );
document.write( "6-unit chord into two parts which are 3 units each. Also the green line\r\n" );
document.write( "is 4 units long because it is the x-coordinate of the center.\r\n" );
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document.write( "
\r\n" );
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document.write( "Now we can use the Pythagorean theorem on either of the two right\r\n" );
document.write( "triangles that the isosceles tringle was split into:\r\n" );
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document.write( "r² = 3² + 4²\r\n" );
document.write( "r² = 9 + 16\r\n" );
document.write( "r² = 25\r\n" );
document.write( " r = 5\r\n" );
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document.write( "
\r\n" );
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document.write( "Since the center is r=5 and the center is (h,k) = (4,5), the equation is\r\n" );
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document.write( "(x - h)² + (y - k)² = r²\r\n" );
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document.write( "or\r\n" );
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document.write( "(x - 4)² + (y - 5)² = 5² or\r\n" );
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document.write( "(x - 4)² + (y - 5)² = 25\r\n" );
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document.write( "Edwin
\r
\n" );
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document.write( " \n" );
document.write( "![\"\"](\"/images/stars/stars-12.gif\")
