Work out tangent to a circle instantly with clear inputs, formula shown and shareable results.
A tangent meets the radius at 90°, so the centre, the point of tangency and the external point form a right triangle. The tangent length is therefore √(d² − r²), and both tangents from an external point are equal.
Tangent length
t = √(d² − r²)
Half-angle at the point
sin(θ/2) = r / d
√(169 − 25) = 12, the classic 5-12-13 triple.
The point is on the circle, the tangent length collapses to zero and only one tangent exists.