Question

Биссектриса равностороннего треугольника равна 12 см. Найдите радиус окружности,вписанной в этот треугольник. В течение 30 минут ответ нужен , так же будет аналогичная задача и вы сможете решить ее.

Answer 1

Биссектриса равностороннего треугольника является медианой и высотой. Тогда радиус вписанной окружности в треугольник равен 1/3 высоты

То есть: r = h/3 = 12/3 = 4 см.

Ответ: 4 см.

Answer 2

Finding the Radius of the Inscribed Circle in an Equilateral Triangle

To find the radius of the circle inscribed in an equilateral triangle, we can use the formula:

radius = (side length of the equilateral triangle) / (2 * tan(π/3))

Given that the bisector of the equilateral triangle is 12 cm, we can find the side length of the triangle by doubling the length of the bisector. Therefore, the side length of the equilateral triangle is 24 cm.

Now, let's calculate the radius of the inscribed circle using the formula mentioned above:

radius = (24 cm) / (2 * tan(π/3))

To calculate the value of tan(π/3), we can use the fact that tan(π/3) = √3.

radius = (24 cm) / (2 * √3)

Simplifying the expression:

radius = 12 cm / √3

To rationalize the denominator, we multiply both the numerator and denominator by √3:

radius = (12 cm / √3) * (√3 / √3) = (12√3 cm) / 3 = 4√3 cm

Therefore, the radius of the circle inscribed in the equilateral triangle is 4√3 cm.

Please note that the answer provided is based on the given information and the formula for finding the radius of the inscribed circle in an equilateral triangle.