Question 992326
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Please help me with this! Show that the two circles (x - 3)^2 + (y-4)^2 = 25 and (x-1)^2 + (y-5/2)^2 =225/4. touch each other.
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The first equation is for the circle of the radius  r = 5  with the center at the point  (x,y) = (3,4).


The second equation is for the circle of the radius  R = {{{15/2}}} = {{{7.5}}}  with the center at the point  (x,y) = (1, {{{5/2}}}) = (1, 2.5).


The distance between the centers is  d = {{{sqrt((3-1)^2 + (4-2.5)^2)}}} = {{{sqrt(2^2+1.5^2)}}} = {{{sqrt(4 + 2.25)}}} = {{{sqrt(6.25)}}} = {{{2.5}}}.


Notice that the second circle is larger than the first one,  and the center of the first circle is located 

inside of the second circle. &nbsp;See the <U>Figure</U> below.


Now notice that R = d + r: &nbsp;&nbsp;7.5 = 2.5 + 5.


It means that the first circle touches the second one from the inside.

<TABLE> 
  <TR>
  <TD> 

{{{drawing( 330, 330, -7.5, 10.5, -5.5, 10.5,
           grid(1),
           circle (3, 4, 5),
           circle (3, 4, 0.2),
           red(circle (1, 5/2, 15/2)),          
           red(circle (1, 5/2, 0.2))

)}}}


  </TD>
  </TR>
</TABLE>