View source for 2008 UNCO Math Contest II Problems/Problem 6

== Problem ==



Points <math>A</math> and <math>B</math> are on the same side of
line <math>L</math> in the plane. <math>A</math> is <math>5</math> units away
from <math>L, B</math> is <math>9</math> units away from <math>L</math>.
The distance between <math>A</math> and <math>B</math> is <math>12</math>. For
all points <math>P</math> on <math>L</math> what is the smallest
value of the sum <math>AP + PB</math> of the distances
from <math>A</math> to <math>P</math> and from <math>P</math> to <math>B</math> ?

<asy>
draw((-1,0)--(16,0),arrow=Arrow());
draw((16,0)--(-1,0),arrow=Arrow());
draw((2,0)--(2,5)--(2+sqrt(128),9)--(2+sqrt(128),0),black);
draw((2,5)--(8,0)--(2+sqrt(128),9),dashed);
dot((2,5));dot((8,0));dot((2+sqrt(128),9));
MP("A",(2,5),W);MP("P",(8,0),S);MP("B",(2+sqrt(128),9),E);MP("L",(14,0),S);
MP("5",(2,2.5),W);MP("12",(2+sqrt(128)/2,7),N);MP("9",(2+sqrt(128),4.5),E);
</asy>

== Solution ==


== See Also ==
{{UNCO Math Contest box|n=II|year=2008|num-b=5|num-a=7}}

[[Category:Intermediate Geometry Problems]]