ratioanalytic geometryrotationgeometrypower of a pointPythagorean Theorem
Problem Statement
If circular arcs AC and BC have centers at B and A, respectively, then there exists a circle tangent to both AC⌢ and BC⌢, and to AB. If the length of BC⌢ is 12, then the circumference of the circle is
[asy]unitsize(4cm);
defaultpen(fontsize(8pt)+linewidth(.8pt));
dotfactor=3;pair O=(0,.375);
pair A=(-.5,0);
pair B=(.5,0);
pair C=shift(-.5,0)*dir(60);
draw(Arc(A,1,0,60));
draw(Arc(B,1,120,180));
draw(A--B);
draw(Circle(O,.375));
dot(A);
dot(B);
dot(C);
label("A",A,SW);
label("B",B,SE);
label("C",C,N);[/asy]<spanclass=′latex−bold′>(A)</span>24<spanclass=′latex−bold′>(B)</span>25<spanclass=′latex−bold′>(C)</span>26<spanclass=′latex−bold′>(D)</span>27<spanclass=′latex−bold′>(E)</span>28