Tangent Lines to Circles Calc ٤‫+‬

Tangent Lines to Circles Calculator is a mathematics calculator used to quickly and easily find angles and the lengths of two lines that are tangent to a circle.

Features:
• Instant calculation.
• The result is copyable to another app.
• The formula is included as a reference.
• Supports up to 16 decimal places.
• Supports various units 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 enter at least two of the following 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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