Arc of the circle through the given points as a Circle running from the smallest of their angles about the centre to the largest
CircularArcThrough[{p1, p2, …}]
CircularArcThrough[{p1, p2, …}, q]
CircularArcThrough[{p1, p2, …}, q, r]
ArcLength[CircularArcThrough[{{(1/2), (Sqrt[3]/2)}, {-(1/2), (Sqrt[3]/2)}, {-1, 0}}]]
→ (2*Pi)/3CircularArcThrough[{{0, 0}, {1, 0}, {0, 1}}]
→ Circle[{1/2, 1/2}, 1/Sqrt[2], {(3*Pi)/4, (7*Pi)/4}]CircularArcThrough[{{1, 0}, {1, 1 / Sqrt[2]}, {0, 1}}]
→ Circle[{1/(2*Sqrt[2]), 1/(2*Sqrt[2])}, Sqrt[-4 + 5*Sqrt[2]]/(2*2^(1/4)), {ArcTan[1/(2*Sqrt[2]*(1 - 1/(2*Sqrt[2])))], 2*Pi - ArcTan[1/(2*Sqrt[2]*(1 - 1/(2*Sqrt[2])))]}]