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Two parallel chords in a circle have lengths 6 and 8. The distance between them is 1. Find the diameter of the circle.

 Jan 4, 2021
 #1
avatar+114094 
+2

We can form two right triangles

 

The longer chord is  closer to the center

 

So....if we  bisect both chords with a radii drawn from the center  we  have  that

 

r^2 =  sqrt  [ x^2  + 4^2]     where x is the  distance  from  the  center to the bisection point

 

Also......we  can  

 

r^2  = sqrt  [ ( x + 1)^2   + 3^ 2]

 

Set  these equal

 

sqrt  [ ( x^2 + 4^2 ]   =  sqrt  [ (x + 1)^2  + 3^2 ]    square  both sides  and simplify

 

x^2 + 16  = x^2  + 2x + 1  + 9

 

2x  = 6

 

x  = 3

 

The  radius =  sqrt  (3^2  + 16] =  sqrt (25)  =  5

 

The diameter = 2*5  = 10

 

 

 

cool cool cool

 Jan 4, 2021
 #2
avatar+824 
+3

Two parallel chords in a circle have lengths 6 and 8. The distance between them is 1. Find the diameter of the circle.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

AB = 6         CD = 8         MN = 1

 

32 + (NO + 1)2 = 42 + NO2          NO = 3

 

Diamater     D = 2* sqrt(NO2 + 42) = 10 units

 

 Jan 4, 2021

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