Tangent of a Circle Calculator

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Single mode finds the tangent length from one external point. Two-circle mode finds common external and internal tangent lengths between two circles.
The radius of the circle.
units
The straight-line distance from the circle centre O to the external point P. Must be greater than the radius.
units
Tangent length (L)
12units

Length of the tangent segment from the external point to the point of tangency

Angle between tangents (2α)45.24degrees
Half-angle at P (α)22.62degrees

Tangent length is 12.0000 units, angle between tangents is 45.24°.

  • The tangent segment is 12.0000 units long.
  • The external point P is 13 units from the centre, so the tangent covers 92.3% of that distance.
  • The half-angle at P is 22.62°, so the two tangent lines spread 45.24° apart.
  • As the external point moves closer to the circle, the tangent length shrinks to zero when d equals r.

Next stepThe power of the point equals L² = d² − r². This value is constant for any chord through P, not just the tangent.

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