50 points,
in triangle def, de = 5, df = 6, and ef = 7. circles are drawn centered at d, e, and f, so that the circles are pairwise externally tangent. find the sum of the areas of the three circles.

Sum of the areas of the three circles is 91.06 units².

Step-by-step explanation:

Given:

Let the  radius of the circle with center D  = x

Let the radius  of the circle with center E  = y  

Let the radius  of the circle with center F  = z

To Find:

Sum of the areas of the three circles = ?

Solution:

So we have these equations

Subtract the second equation from the  first  and we have that

Add this to equation to the third equation  and we have that

Now we have Area of Circle

Substituting Radius we get

∴