Cotangent theorem calculator

Theorem in geometry is a proof - an argument establishing a property. A theorem is a statement that proves some property and requiring establishment. Theorems are also called lemmas, properties, consequences, rules, signs, affirmations.

To help you calculate the cotangent theorem, we have created a simple cotangent theorem calculator. To use it, simply enter the known values in the input boxes, and our calculator will automatically calculate unknown value.

Cotangent Theorem Formula

The cotangent theorem connects the sides of a triangle and the angle between them with the radius of a circle inscribed in this triangle as follows - the difference between the half-perimeter and one of the sides, divided by the cotangent of half of the angle opposite to it, is equal to the radius of the inscribed circle. The proof of the cotangents theorem consists in using algebraic and trigonometric transformations to derive the necessary radical from a given relation in an arbitrary triangle. The cotangent theorem formula is:

\dfrac{p-a}{ctg\left(\dfrac{\alpha}{2} \right)} = \dfrac{p-b}{ctg\left(\dfrac{\beta}{2} \right)} =\dfrac{p-c}{ctg\left(\dfrac{\gamma}{2} \right)} = r

Conclusion

Calculating the cotangent theorem can be complex, but our cotangent theorem calculator and formula make it easy for you. Simply enter the values and let our calculator do the rest for you. Try it out for yourself and see how easy it can be!