The okrąg wpisany i opisany na trójkącie (inscribed and circumscribed circles of a triangle) are fundamental concepts in geometry. These circles provide important relationships between a triangle's sides, angles, and area. The formulas for calculating the radii of these circles vary depending on the type of triangle, such as trójkąt prostokątny (right triangle), trójkąt równoramienny (isosceles triangle), or trójkąt równoboczny (equilateral triangle).
• The center of the inscribed circle lies at the intersection of the triangle's angle bisectors.
• For a right triangle, the radius of the circumscribed circle is half the length of the hypotenuse.
• In an isosceles triangle, the radius of the circumscribed circle is related to the triangle's height and base.
• For an equilateral triangle, both the inscribed and circumscribed circle radii can be expressed in terms of the side length.
• The general formula for the area of a triangle using the semiperimeter is applicable to all triangle types.
