Tests if the [x,y] point is inside a closed arc.

var arc={
    cx:150, cy:150,
    innerRadius:75, outerRadius:100,
    startAngle:0, endAngle:Math.PI
}

function isPointInArc(x,y,arc){    
    var dx=x-arc.cx;
    var dy=y-arc.cy;
    var dxy=dx*dx+dy*dy;
    var rrOuter=arc.outerRadius*arc.outerRadius;
    var rrInner=arc.innerRadius*arc.innerRadius;
    if(dxy<rrInner || dxy>rrOuter){return(false);}
    var angle=(Math.atan2(dy,dx)+PI2)%PI2;
    return(angle>=arc.startAngle && angle<=arc.endAngle);
}