Sandy J.

asked • 11/14/15

area of circle

In a circle two chords are given which parallel.Mid point of AB is M and that of CD is N AB=12 cm , CD=16cm and OM=8 cm .Find ON.

Mark M.

Assuming O is the center, are the two chords on the same side of O or on different sides?
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11/14/15

1 Expert Answer

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Arthur D. answered • 11/14/15

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draw a circle
draw chord AB with midpoint M (draw horizontally)
draw chord CD parallel to AB with midpoint N
draw segment MN through center O
draw segment (radius) OB
MB=6 cm
MO=8 cm
using Pythagorean Theorem...
OB2=82+62
OB2=64+36=100
OB=10 cm
draw OC which is also a radius and together with OB forms a diameter (CB)
OC=10 cm
CN=8 cm
using Pythagorean Theorem...
102=82+ON2
100=64+ON2
100-64=ON2
36=ON2
ON=6 cm
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Mark M.

Your direction, "draw segment MN through center O" assumes that the two chords are on opposite sides of the center O.
Would the distances be different if the two chords were on the same side of O?
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11/14/15

Arthur D.

tutor
Hi Mark,
           Correct me if I'm wrong. If the chords are on the same side of center O, then OB and OD are both radii.
 If MO=8 then OB is 10. Therefore OD, being a radius also, would be 10 as well. If OD=10, ND=8, then NO must equal 6. My diagram has the two chords above the center O as compared to below the center O so you can see how I'm getting my numbers. It seems that the only difference would be that MN=14 if the chords are on opposite sides of the center and MN=2 if the chords are on the same side of center O.
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11/14/15

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