Equation of lines tangent to circle

Happen to work up my own solution to this the other day, so I'm posting it here. This was intended to plug into a spreadsheet. It's probably less elegant than possible and less complete than needed, but, oh well.

It's assumed that all points are co-planar, so nothing fancy going on here. Refer to the illustration above. Clicking it should return a larger (readable) version.

Given:
• a circle, (x - h)² + (y - k)² = r²,
with center at (h, k) and radius r; and
• a point at (p, q) outside the circle:
Find:
• the coordinates of the tangent point(s), and
• the equation(s) of the tangent line(s) from the point to the circle.

Through any given outside point, there are two possible tangent lines to a given circle, but once you find one, finding its doppelgängers is just a matter of changing a few signs.
Let Δ = ±1 to express that sign change.

Let ∆ABC be such that:
• A is the vertex at (h, k), which is the center of the given circle,
• B is the vertex at given point at (p, q), and
• C is the tangent point.

Notice that ∆ABC is a right triangle by definition because any tangent line is perpendicular to the radius at the point of intersection.

So:

c = AB (the hypotenuse as shown) = √([p - h)² + (q - k)²]
α = ∠CAB = acos[r / c]
β = ∠ABC = asin[r / c] — reference only, not used in these calculations
γ = ∠BCA = π/2 — reference only, not used in these calculations
δ = acos[(p - h) / c]
(if you are wondering, α is "alpha," β is "beta,"  γ is "gamma," δ is small "delta," and Δ is capital "delta.")
δ is just used for the angle between the x-axis and c.
(See: Convert cartesian ↔ polar coordinates for some more details if you like.)

Tangent Point C_Δ:
Δ = ±1
x = r · cos[α + Δδ] + h, and
y = Δr · sin[α + Δδ] + k

Tangent Line, y = m_Δx + b_Δ:
Δ = ±1
m_Δ = –Δ/tan[α + Δδ], and
b_Δ = Δ(r · cos[α + Δδ] + h) / tan[α + Δδ] + Δr · sin[α + Δδ] + k

Sample Calculation
Given:
Circle: (x - 0.6)² + (y - 0.5)² = 1.5625
Point: (-0.625, 2.25)
h = 0.6; k = 0.5; r = 1.25
p = -0.625; q = 2.25
δ ≈ 2.18152
α ≈ 0.94571

Δ=1:Tangent Point: (-0.6499, 0.5179); Tangent Line: y = 69.641x +45.7756

Δ=-1:
Tangent Point: (1.0109, 1.6805); Tangent Line: y = -0.3481x +2.0324