Question 985461
The center point of the circle is equally distant from both X and Y, forming an isosceles triangle; but since you have central angle being 60 degrees, this forces the other angles each to also be 60 degrees.  This is then an equilateral triangle with points, X, Y, and the center of the circle.  The radius will be the DISTANCE between  X and Y, found using the distance formula.  Now you know radius r.


{{{r=sameAs=sqrt((9-3)^2+(1-4)^2)}}}
{{{r=sqrt(36+9)}}}
{{{r=sqrt(45)}}}
{{{r=3sqrt(5)}}}


Next, simply form {{{(6/36)(2pi*r)}}} and compute or evaluate the length of arc.
(Fraction of the circumference)