Question 1006852
.
Find the length of the common external tangents to two circles of radii 5 cm and 12 cm respectively, if the distance between their centers 25 cm.
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The length of the common external tangents to two circles is


{{{sqrt(25^2 - (12-5)^2)}}} = {{{sqrt(625 - 49)}}} = 24 cm.


See the Figure below.

<TABLE> 
  <TR>
  <TD>

&nbsp;&nbsp;&nbsp;&nbsp;{{{drawing( 300, 260,  -6.5, 8.5, -6.5, 6.5, 
            circle( 0.0, 0.0, 6.0), 
            circle( 5.0, 0.0, 3.0), 

            line( 0.0, 0.0, 5.0, 0.0),
       blue(line( 0.0, 0.0, 3.6, 4.8)),
       blue(line( 5.0, 0.0, 6.8, 2.4)),
      green(line( 2.4, 5.7, 8.0, 1.5)),

            locate(-0.3, 0.0, P),
            locate( 4.8, 0.0, Q),

            locate( 3.4, 5.6, A),
            locate( 6.6, 3.3, B),

            locate( 1.4, 3.6, r1),
            locate( 6.2, 1.8, r2)
)}}} 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 1</B>.

 </TD>
  <TD>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{drawing( 300, 260,  -6.5, 8.5, -6.5, 6.5, 
            circle( 0.0, 0.0, 6.0), 
            circle( 5.0, 0.0, 3.0), 

        red(circle( 0.0, 0.0, 3.0)), 

            line( 0.0, 0.0, 5.0, 0.0),
       blue(line( 0.0, 0.0, 3.6, 4.8)),
       blue(line( 5.0, 0.0, 6.8, 2.4)),
      green(line( 2.4, 5.7, 8.0, 1.5)),

            locate(-0.3, 0.0, P),
            locate( 4.8, 0.0, Q),

            locate( 3.4, 5.6, A),
            locate( 6.6, 3.3, B),

             arc( 3.6, 4.8, 0.9, 0.9, 35, 122),
             arc( 3.6, 4.8, 1.2, 1.2, 35, 122)

             arc( 6.8, 2.4, 0.9, 0.9, 35, 122),
             arc( 6.8, 2.4, 1.2, 1.2, 35, 122),

        red(line( 1.8, 2.4, 5.0, 0.0)),

            locate( 1.8, 4.2, r1),
            locate( 6.2, 1.8, r2),

            locate(-0.5, 1.6, r1-r2),

            locate( 1.5, 3.2, C)
)}}} 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 2</B>. 

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

For details see the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-construct-a-common-exterior-tangent-line-to-two-circles.lesson>HOW TO construct a common exterior tangent line to two circles</A>&nbsp; in this site.