Question 201686: TWO CIRCLES TOUCH EXTERNALLY.THE SUM OF THEIR AREA IS 130 sq cm AND DISTANCE BETWEEN THIER CENTRES IS 14 cm .FIND THE RADII OF CIRCLES....?
I'LL BE THANKFUL.....
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
And I will be both pleased and thankful if you stop typing your messages in ALL CAPS. All caps is the electronic equivalent of shouting and is therefore both annoying and rude.
Furthermore, I suspect that the sum of the areas of the two circles in your problem is actually  instead of  as stated.
Going on that presumption, if the centers, or centres if you insist, are separated by a distance of 14 cm, then the point of tangency where the two circles touch is also the end point of a radius for each of the circles. Hence the sum of the measures of the radii for the two circles is 14 cm.
Let  represent the measure of the radius of one of the circles, then  must represent the radius of the other circle. Furthermore, the area of the first circle is  , the area of the second circle is ^2) , and we are given that the sum of these areas is . Hence:
^2 = 130\pi)
^2 = 130)
(r - 11) = 0)
 or 
One radius is 3 and the other is 11.
Now, if my assumption about the given area was wrong, then you would end up with the following computational horror:
}}{2} )
Which, by the way, is a conjugate pair of complex numbers which tells me that the solution is impossible if the combined area is only instead of a little over 3 times that value. In fact, the maximum possible sum of the radii of two circles with a combined area of is 
John
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