document.write( "Question 1056900: Find the value/s of k for which the circle x^2+y^2=4 and (x-4)^2 + (y-3)^2=k^2 intersect at exactly one point. \n" ); document.write( "

Algebra.Com's Answer #671981 by MathTherapy(10553) $\"\"$ $\"About$

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Find the value/s of k for which the circle x^2+y^2=4 and (x-4)^2 + (y-3)^2=k^2 intersect at exactly one point.
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Since the circles INTERSECT at just 1 point, it obviously means that they only TOUCH each other at a point on the OUTSIDE of their circumferences
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document.write( "The 1st circle: [] is centered at the origin (0, 0), and has a radius of r = 2 ()
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document.write( "The 2nd circle: [] is centered at (4, 3) and has a radius of r = k
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document.write( "Since the circles touch each other at 1 point, and the 2nd circle’s center is (4, 3), it follows that they MUST TOUCH each other in the 1st quadrant 
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document.write( "When joined, the centers of the 2 circles form the 2 radii of the circles, and these radii, combined, happen to form the hypotenuse of a 3-4-5 right triangle. This hypotenuse = 5\r
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document.write( "Since the circle centered at (0, 0) has a radius of 2, it follows that the circle that’s centered at (4, 3) has a radius of 5 – 2, or 3, so \r
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document.write( "The 2nd circle: [], centered at (4, 3), can also be much larger than the circle centered at (0, 0), and so, can have a  (3 + 2 + 2), or 3, 
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document.write( "plus the diameter of the circle centered at (0, 0). This means that the smaller circle [centered at (0, 0)] will be inscribed in the larger circle.\r
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document.write( "If it's confusing, you'd see a much clearer picture if you draw a diagram, as I did.
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document.write( "It's as easy as that...nothing COMPLEX! \n" );
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