Think about three circles that contact one another on the outside and have radii of 2 cm, 3 cm, and 4 cm. Calculate the triangle's perimeter, which is created by connecting these circles' centres.
Question
Think about three circles that contact one another on the outside and have radii of 2 cm, 3 cm, and 4 cm. Calculate the triangle's perimeter, which is created by connecting these circles' centres.
Solution
To calculate the perimeter of the triangle formed by the centers of the three circles, we first need to find the lengths of the sides of the triangle.
The length of each side of the triangle is equal to the sum of the radii of the two circles it connects.
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The first side connects the circles with radii 2 cm and 3 cm. So, its length is 2 cm + 3 cm = 5 cm.
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The second side connects the circles with radii 2 cm and 4 cm. So, its length is 2 cm + 4 cm = 6 cm.
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The third side connects the circles with radii 3 cm and 4 cm. So, its length is 3 cm + 4 cm = 7 cm.
Finally, to find the perimeter of the triangle, we add up the lengths of its sides:
Perimeter = 5 cm + 6 cm + 7 cm = 18 cm.
So, the perimeter of the triangle formed by the centers of the three circles is 18 cm.
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