Two parallel chords in a circle have lengths 6 and 8. The distance between them is 1. Find the diameter of the circle.
+129918 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
+1641 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
