Question 1158589
Drew picture not shown here, distance from center to the chord,  {{{2sqrt(11)}}}.  See a right triangle,  hypotenuse 12 same as radius, leg 10 units.


An angle measure  betwen the described distance and the hypotenuse, {{{arctan(10/(2sqrt(11)))}}}; and you want TWICE this angle:  112.88 degrees.


The major arc is  247.11 degrees.