Trigonometric solutions that relate geometrical quantities of the triangle and the inscribed circle
DOI:
https://doi.org/10.5902/2179460X75968Keywords:
Existence, Geometrical quantities, Polynomial equations, Trigonometric solutionsAbstract
This paper is concerned with the relations between a triangle and its inscribed circle. We obtained a specific class of trigonometric solutions that determine the area of the triangle from the radius of the inscribed circle and from two fixed sides of the triangle. To prove our results, we use trigonometric relations from Euclidean geometry, Viète formulas for roots of polynomial functions, Lagrange multipliers and Differential Calculus in one and two variables. In addition, we explain the behavior of these solutions through computer simulations including the intervals of existence and specific numerical cases. Moreover, we describe the relations between the triangle area and the inscribed circle area.
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