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# geometry question

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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
+117576
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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

Jan 4, 2021
#2
+1164
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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.

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

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