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FilledCurve

FilledCurve[{segments__}]

where segments can be Line, BezierCurve. For example

a = {{-1, 0}, {0, 1}, {1, 0}}; b = {{0, -(2/3)}, {-1, 0}};
Graphics[FilledCurve[{BezierCurve[a], Line[b]}]]

One can fill the shape defined by components using following pattern

FilledCurve[{components__List}]

For example

pts = {{0, 1}, {-1, -(1/2)}, {1, -(1/2)}};
Graphics[FilledCurve[{{Line[2 pts]}, {Line[pts]}}]]
note

It uses even-odd rule for filling. The intersection will not be filled.