Question 1205673
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Let A be the center of the circle with radius 5cm and B be the center of the circle with radius 8cm.<br>
Since the distance between the centers is 13cm, the two circles are tangent to each other.<br>
Draw the common external tangent CD, with C and D being the points of tangency with circles A and B respectively.  The radii AC and BD are both perpendicular to the tangent CD.<br>
Let point E be on radius BD so that AE is parallel to the tangent CD.  ACDE is then a rectangle, with one dimension 5 cm and the other dimension equal to the length of the common external tangent.<br>
Use the Pythagorean Theorem on right triangle ABE to find the length of the other dimension of the rectangle and thus the length of the external common tangent.<br>
{{{x^2+3^2=13^2}}}
{{{x^2+9=169}}}
{{{x^2=160}}}
{{{x=sqrt(160)=4*sqrt(10)}}}<br>
ANSWER: {{{4*sqrt(10)cm}}}<br>