Tangent Lines to Circles Calculator are mathematics calculator to find angles and the length of two lines that are tangent to a circle fast and easy.

Features:
• Instant calculation.
• The result is copy able to another app.
• The formula is included as reference.
• Support up to 16 decimal places.
• Support various unit for each input.

Two congruent right triangles are formed, since the tangent line is perpendicular to the radius.
So line AB has the same length as line BC.
And the radius AD has the same length as DC.
∠ABC Angle x° = 180° - Angle y°, or
∠ADC Angle y° = 180° - Angle x°

Formula:
Pythagorean theorem
DB = √AD² + AB²

sin (x/2) = DA / DB
cos (x/2) = AB / DB
tan (x/2) = DA / AB

Inputs:
1. Angle [x°]
2. Angle [y°]
3. Length [AD][DC]
4. Length [AB][BC]
5. Length [DB]

Quick Guide:
Clear the input and at least key in these two parameters to get results:
1 & 3 Angle [x°] & Length [AD][DC]
1 & 4 Angle [x°] & Length [AB][BC]
1 & 5 Angle [x°] & Length [DB]
2 & 3 Angle [y°] & Length [AD][DC]
2 & 4 Angle [y°] & Length [AB][BC]
2 & 5 Angle [y°] & Length [DB]
3 & 4 Length [AD][DC] & Length [AB][BC]
3 & 5 Length [AD][DC] & Length [DB]
4 & 5 Length [AB][BC] & Length [DB]

Tangent lines to circles. In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.

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