what is the diameter of three circle inscribed in a triagle whose base is 50 cm.
To find the diameter of three circles inscribed in a triangle, we need to consider the properties of an inscribed circle.
First, let's define a few terms:
- Incenter: The incenter is the center point of the inscribed circle, which is equidistant from all three sides of the triangle.
- Inradius: The inradius is the radius of the inscribed circle.
In a triangle, the incenter is the intersection point of the three angle bisectors. In this case, we have three circles inscribed in the triangle, with their centers coinciding at the incenter.
Since the base of the triangle is 50 cm, we can utilize the inradius and the formula for the length of the base to find the diameter of each circle. Let's proceed step by step:
1. Find the length of the inradius:
- Using the formula for the area of a triangle: Area = (semiperimeter) * (inradius)
- The semiperimeter is half the sum of the triangle's three sides: Semiperimeter = (a + b + c) / 2
- For our triangle, two sides are equal, so let's assign the length of the base as 'a'. Therefore, the semiperimeter is Semiperimeter = (50 + a + a) / 2 = (50 + 2a) / 2
- The area of the triangle can be calculated using Heron's formula or other appropriate methods.
- Once you have the area, solve for the inradius: Inradius = Area / Semiperimeter
2. Find the diameter of the circle:
- The diameter of a circle is twice the radius.
- Therefore, the diameter of each circle inscribed in the triangle is Diameter = 2 * Inradius
By following these steps, you should be able to find the diameter of the three circles inscribed in the triangle based on the given length of the base.