ad 
be two circles intersecting at 
and 
The tangent like closer to 
touches 
and 
respectively. If 
and 
find 
Y by Adventure10, Mango247
A triangular corner with side lengths 
is cut from equilateral triangle 
of side length 
. The perimeter of the remaining quadrilateral is
![[asy]
draw((0,0)--(2,0)--(2.5,.87)--(1.5,2.6)--cycle, linewidth(1));
draw((2,0)--(3,0)--(2.5,.87));
label("3", (0.75,1.3), NW);
label("1", (2.5, 0), S);
label("1", (2.75,.44), NE);
label("A", (1.5,2.6), N);
label("B", (3,0), S);
label("C", (0,0), W);
label("D", (2.5,.87), NE);
label("E", (2,0), S);[/asy]](//latex.artofproblemsolving.com/c/8/3/c83a21ce759a694a577eb8fc114c18cc14a92710.png)
is cut from equilateral triangle 
of side length 
. The perimeter of the remaining quadrilateral is![[asy]
draw((0,0)--(2,0)--(2.5,.87)--(1.5,2.6)--cycle, linewidth(1));
draw((2,0)--(3,0)--(2.5,.87));
label("3", (0.75,1.3), NW);
label("1", (2.5, 0), S);
label("1", (2.75,.44), NE);
label("A", (1.5,2.6), N);
label("B", (3,0), S);
label("C", (0,0), W);
label("D", (2.5,.87), NE);
label("E", (2,0), S);[/asy]](http://latex.artofproblemsolving.com/c/8/3/c83a21ce759a694a577eb8fc114c18cc14a92710.png)
because we are adding 1 and subtracting 2 from the triangle's perimeter.
which is just![\[ AC+CE+ED+DA=3+2+1+2=\boxed{\textbf{(E)} \ 8}. \ \blacksquare\]](http://latex.artofproblemsolving.com/6/4/b/64bdfd779f0b9b2fd6d98a5ade5b961f6865395c.png)
