SOLUTION: Two parallel chord lies on opposite sides of the centre of a circle of diameter 24cm.the length of the chords are 5cm and 6cm. Calculate the distance between the two chords?

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Question 776923: Two parallel chord lies on opposite sides of the centre of a circle of diameter 24cm.the length of the chords are 5cm and 6cm. Calculate the distance between the two chords?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
One way to handle this is lay the circle onto a cartesian system, centered at the origin, radius of the circle 12 cm. Examine the two chords separately.

x%5E2%2By%5E2=12%5E2
y%5E2=12%5E2-x%5E2
highlight%28y=sqrt%2812%5E2-x%5E2%29%29

The two lengths for x to examine for y are HALF of 5 cm, and HALF of 6 cm. Evaluate for each, separately, and then SUM the two results for y. This result is the distance between the two chords.


This picture shows x=2.5, corresponding to a chord length of 5 cm. The equation for the circle is shown in the symbolic description already described. The value for y is the distance of the chord from the diameter. The diameter here is shown as the horizontal axis from -12 to +12. The distance is computed as y=sqrt%28144-2.5%5E2%29.
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A similar picture and process is done for the 6 cm. chord.