document.write( "Question 1082466: A circle has a center (0,9) and radius 9. A second circle with radius 4, touches the first circe and the x-axis
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Algebra.Com's Answer #696606 by ikleyn(52927) $\"\"$ $\"About$

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\n" ); document.write( "A circle has a center (0,9) and radius 9. A second circle with radius 4, touches the first circe and the x-axis
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\n" ); document.write( "b) Find the possible equations for the second circle if it does not lie in the first quadrant
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document.write( "0.  Make a sketch to follow my arguments.\r\n" );
document.write( "    Let A and B be the centers of the circles (A lies at y-axis).\r\n" );
document.write( "    Connect the points A and B by the straight segment.\r\n" );
document.write( "    From the point B draw the horizontal straigh line till the intersection with y-axis.\r\n" );
document.write( "    Let C be the intersection point with y-axis.\r\n" );
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document.write( "1.  Then you have a right-angled triangle ABC.\r\n" );
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document.write( "    The length of AB is |AB| = 9 + 4 = 13 units.   (Since \"a second circle with radius 4 touches the first circle\"\r\n" );
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document.write( "    The length of AC is |AC| = 9-4 = 5 units.      (Since \"a second circle with radius 4, touches the x-axis\")\r\n" );
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document.write( "2.  Hence, the length of BC is |BC| =  = 12 units.\r\n" );
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document.write( "3.  Thus the center of the second circle is at the point (x,y) = (12,4).\r\n" );
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document.write( "4.  Now, the equation of the second circle is \r\n" );
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document.write( "     = ,   or, which is the same,    = 16.\r\n" );
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