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please include an explanation! thank you

 Mar 1, 2020
 #1
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+2

There is this famous formula that you should remember in the future:

r = radius

 

4r^2 =2^2 + 6^2 + 3^2 + 4^2

4r^2 = 4     +  36   +   9    +   16

4r^2 = 65                Divide both sides by 4

r^2   =16.25            Take the square root of both sides

r  = sqrt(16.25)

r =~4.0311  x  2 =~8.0622 - The diameter of the circle.

 Mar 1, 2020
 #2
avatar+21955 
+2

If you don't remember the formula, you can do it this way.

 

The perpendicular bisector of AB will go through the center of the circle;

also, the perpendicular bisector of CD will go through the center of the circle.

This means that the center of the circle in the intersection of these two lines.

 

Place the diagram onto a graphing plane so that the origin of the plane is the midpoint of CD.

The coordinates of D are (4,0) and the coordinates of C are (-4,0).

Also, the coordinates of A are (2,3) and the coordinates of B are (2,-4).

 

The center of the circle must be on the y-axis (the perpendicular bisector of CD) and also on the horizontal line that passes through

the midpoint of AB; this point has a y-value of -0.5.

Therefore, the center of the circle occurs at (0, -0.5).

 

To find the radius of the circle, find the distance from this center point to any of the points A, B, C, or D.

Finding the distance from the center to point D:  radius  =  sqrt[ (4-0)2 + (0 - -0.5)2 ]  =  sqrt( 42 + 0.52)

                                                                             radius  =  sqrt(16.25)

 

So, the diameter  =  2·sqrt(16.25)

 Mar 2, 2020
 #3
avatar+1090 
+3

AP = 3      BP = 4     CP = 6     DP = 2

CD =  CP + DP = 8     ( Long side of a rectangle )

BP - AP = 1             ( Short side of a rectangle )

Diagonal of this rectangle is the diameter of the circle.

 

Diameter     D = sqrt [(CD²) + ( 1² )]  = 8.062257748 units   indecision

 Mar 2, 2020
 #4
avatar+1090 
+4

Bravo, guys!  You've just proved that " all roads lead to Rome"   laugh

 Mar 2, 2020

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