SOLUTION: AB and CD are two parallel chords of a circle such that AB = 24 cm and CD= 10 cm. If the radius of the circle is 13 cm , find the distance between the chords. My solution :- Cons

Question 1110106: AB and CD are two parallel chords of a circle such that AB = 24 cm and CD= 10 cm. If the radius of the circle is 13 cm , find the distance between the chords.
My solution :-
Construction draw a circle with radius 13 cm . Mark two parallel chords AB and CD. Join OB it will make a right angle triangle, so by using Pythagoras theorem
In triangle ONB
OB^2= ON^2 + NB^2
13^2=ON^2 + 12^2
169 - 144 = ON^2
25 sq root = ON
5 = ON
Now in the same way join OD
In triangle OMD
OD^2 = OM^2 + MD^2
13^2 = OM^2 + 5^2
169-25= OM^2
144 sq root = OM^2
12 = OM
Distance between the chords = 12 + 5
17 cm
Experts please check whether my answer is wrong or correct
And check the solution also. I want to know the exact answer

Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
You can make a sketched graph for this circle, center at the point (0,0).
If you make AB and CD segments (chords) perpendicular to y-axis and for convenience, above the x-axis, then you can identify two points on the circle and you know x coordinates but you can find the y-coordinates.

You can start the circle's equation as

Half of AB is so here, x=12.

AMP Parsing Error of [y=sqrt(169-x^2]: Invalid function: opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 88. .

Half of CD is , so here, x=5.

In the described arrangement, chord AB is 5 units from the center, and chord CD is 12 units from the center, both chords perpendicular to the positive y-axis. SEVEN units apart from each other; 12-5=7.

(You can do a similar arrangement but put the two parallel chords on OPPOSITE sides of the origin, and may get a different distance between chords.)
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

This problem has 2 (two, TWO) solutions. If both the chords are in different sides from the center, then the distance between the chords is 12 + 5 = 17, as you determined it. If, in opposite, both the chords are in one side from the center, then the distance between the chords is 12 - 5 = 7, as you can easily to determine it on your own.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Your solution is fine; but it is only one of two possible answers, as suggested in the response by the other tutor.

Radii to the endpoints of the chords, and a diameter perpendicular to the two chords, create right triangles with hypotenuse 13 and legs either 5 or 12 (because the diameter bisects each chord). Then we know the chord of length 24 is 5 from the center of the circle and the chord of length 10 is 12 from the center.

But your answer assumes the chords are on opposite sides of the center of the circle, making the distance between them 12+5=17. The two chords could be on the same side of the center, making the distance between them 12-5=7.
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