The tangent coordinates give inconsistent results for certain situations.
See the code

#import "@preview/cetz:0.4.2"

#cetz.canvas(length:1cm, {
  import cetz.draw: *
  circle((2,2), radius: 2, name:"c")
  let a = "c.0deg"
  circle(a)
  line((a,-1cm,(element:"c", point:a, solution:1)),
    (a,5cm,(element:"c", point:a, solution:1))
  )
})

Which produces

Changing a to "c.10deg" produces

and "c.30deg" errors with Panicked with: "No tangent solution for element c and point \"c.30deg\""

While the panic is probably the "correct" solution, the result at "c.10deg" is maybe the most convenient for drawing things.