The formula for finding the radius of a circle inscribed in a triangle is r = (abc)/(4A), where a, b, and c are the sides of the triangle and A is the area of the triangle.
No, the radius of a circle inscribed in a triangle can never be greater than or equal to the length of any side of the triangle. It will always be less than the length of the shortest side of the triangle.
The area of a triangle can be found by using the formula A = rs, where r is the radius of the inscribed circle and s is the semi-perimeter of the triangle (s = (a+b+c)/2).
Yes, the radius of a circle inscribed in a right triangle is always equal to half the length of the hypotenuse. This is a special case of the general formula mentioned above, where the area of the triangle becomes A = (1/2)(ab).
Yes, the radius of a circle inscribed in an equilateral triangle can be calculated without knowing the length of its sides. It is equal to (2/3) times the height of the triangle, or (2/3)(√3/2)a, where a is the length of any side of the triangle.