SOLUTION: given a circle, draw two chords who's lengths are in the ratio 1:2 and who's distances from the center are in the ration 2:1. Find the length of each chord in terms of the radius '

Algebra ->  Circles -> SOLUTION: given a circle, draw two chords who's lengths are in the ratio 1:2 and who's distances from the center are in the ration 2:1. Find the length of each chord in terms of the radius '      Log On


   

Question 839555: given a circle, draw two chords who's lengths are in the ratio 1:2 and who's distances from the center are in the ration 2:1. Find the length of each chord in terms of the radius 'r' of the circle. Find their lengths if r = 10 cm.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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given a circle, draw two chords who's lengths are in the ratio 1:2
and who's distances from the center are in the ration 2:1.
Find the length of each chord in terms of the radius 'r' of the circle.
:
A right triangles formed by the chords, with sides: half the chord length,
distance from the center, and the radius, which is the hypotenuse.
:
As I examine these, it's apparent that the two triangles are indentical,
one triangle the distance from the center is the longer side and the other
triangle the long side is half the length of the longer chord.
:
On the right triangle let the shorter leg = 2, the longer leg = 2s
The chord will be twice the length of the legs
Find s in terms of r
s^2 + (2s)^2 = r^2
s^2 + 4s^2 = r^2
5s^2 = r^2
s^2 = r%5E2%2F5
s = sqrt%28r%5E2%2F5%29
The shorter chord = 2sqrt%28r%5E2%2F5%29
The longer chord = 4sqrt%28r%5E2%2F5%29
:
"Find their lengths if r = 10 cm."
The shorter chord:
2sqrt%2810%5E2%2F5%29 = 2sqrt%2820%29 = 8.94 cm
The longer chord:
4sqrt%2810%5E2%2F5%29 = 4sqrt%2820%29 = 17.89 cm

The longer chord = 4sqrt%28r%5E2%2F5%29
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