anonymous
  • anonymous
Two different circles that pass through the point (1,3) are tangent to both coordinate axes. If the length of the radius of the smaller circle is "r" and the length of the radius of the larger circle of "R", what is the value of "r+R"?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
trick is that the x and y values of the centers of the circles are the same and are also the same as the radii of the respective circles so (x-r)^2 +(y-r)^2 = r^2 stick in the know point (1-r)^2 = (3-r)^2 = r^2 0 = r^2 -8a +10 solve and r = (8 +-sqrt(24))/2 so r = 6.45 and 1.55 or so so r + R = 8 now I see why they asked for teh sum of the radii. It means you can ignore the sqrt ANS = 8
anonymous
  • anonymous
the line above is wrong. should read (1-r)^2 + (3-r)^2 = r^2

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