By user request on Love2d IRC channel, yesterday I've made this nice function to do intersection/collision check between a ray (for clearance, here, a ray is a infinite line with starting point but no end point) and a circle.

Underlying code is fairly simple, though it does not even require understanding to use the function.

Love2d version takes advantage of multi-return values.
Haxe version has slightly longer code due for more optimal implementation of interface.

Download Haxe .hx Download Love2d .love

Snip:

--[[
Does a ray-circle intersection test.
Parameters:
	x1, y1, di - x, y, direction (radians) of ray
	x, y, r - position & radius of circle
Returns:
	result - whether collision occurred
	x - collision X
	y - collision Y
	distance - distance from ray start to collision point
]]
function ray2circle(x1, y1, di, x, y, r)
	local vx = math.cos(di)
	local vy = math.sin(di)
	
	-- get relative XY of circle (relative to ray origin):
	x = x - x1
	y = y - y1
	
	-- rotate it based on ray direction (as if ray starts at XY=0 and goes at +X):
	local tx = x * vx + y * vy
	local ty = x * vy + y * -vx
	
	-- clear misses:
	if (tx < -r) or (ty > r) or (ty < -r) then
		return false, nil, nil, nil
	end
	
	-- find X coordinate that line hits rotated circle at
	th = math.abs(math.cos(math.asin(ty / r))) * r
	
	-- too far behind
	if (tx + th < 0) then
		return false, nil, nil, nil
	end
	
	-- line start is inside the circle:
	tx = tx - th
	if (tx < 0) then
		return true, x1, y1, 0
	end
	
	--
	return true, x1 + tx * vx, y1 + tx * vy, tx
end