XPY is the circumference minus XY
the angle of arc XY is 90 degrees
a full revolution of a circle is 360 degrees
the distance XY is 1/4 of the circumference of the circle
the circumference of a circle is C=2 pi r
r is 10m
the circumference is 20 pi
1/4 of 20 is 5
the distance of arc XY is 5 pi
20pi - 5 pi = 15 pi