SOLUTION: 6. Two parallel chords 16 centimeters and 30 centimeters long are 23 centimeters apart. Find the length of the radius of the circle.

Question 739886: 6.
Two parallel chords 16 centimeters and 30 centimeters long
are 23 centimeters apart. Find the length of the radius of the
circle.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two parallel chords 16 centimeters and 30 centimeters long are 23 centimeters apart.
Find the length of the radius of the circle.
:
Draw this out
Let x = distance from the center that bisects the nearest Chord, (30 cm).
Draw radii from the center to the ends of the chord
Two identical right triangles are formed, the radii are the hypotenuses
r^2 = x^2 + 15^2
r^2 = x^2 + 225
:
Assume the other chord (16cm), is on the other side of center, therefore distance from the center that bisects that chord (16cm) = 23-x, so we have:
r^2 = (23-x)^2 + 8^2
r^2 = 529 - 46x + x^2 + 64
r^2 = x^2 - 46x + 593
replace r^2 with (x^2+ 225)
x^2 + 225 = x^2 - 46x + 593
x^2 - x^2 + 46x = 593 - 225
46x = 368
x = 368/46
x = 8 cm
Find the radius
r^2 = 8^2 + 225
r^2 = 289
r =
r = 17 cm is the radius
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