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

∴

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step-by-step explanation:

the x's and the y's both go up the same amount each time, therefore it will be a linear function because it will go in a straight line when drawn on a graph.

hope this !

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,