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Imagine you are given circle O with two perpendicular diameters drawn inside, named AC and BD. A chord has one point on point A and is concurrent with diameter AC and the circle. The chord extends to the other side of the circle, passing through diameter BD, ending at point E. The portion of the chord AE from point A to diameter BC has a length of 7 units, and the portion of the chord AE from diameter BD to point E has a length of 3 units. What would be the length of the chord EC?

I started by finding that the diameter AC, chord AE (length 10 units), and chord EC would form a right triangle, so finding the diameter would allow me to solve for chord EC. I am stuck with finding a method to solve for the diameter. The answer, rounded to the nearest tenth, is either 5.2, 6.1, 6.3, 7.1, or 7.6 units. Any help would be appreciated.

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  • $\begingroup$ it will help a lot if you can add a figure. $\endgroup$
    – abel
    Feb 21, 2015 at 18:56
  • $\begingroup$ How would make a figure? I'm sorry, I'm kind of new at this. $\endgroup$
    – John Doey
    Feb 21, 2015 at 19:03
  • $\begingroup$ sorry, i don't know how. i have seen even images from note books posted here. hopefully someone will come along to help you. $\endgroup$
    – abel
    Feb 21, 2015 at 19:06

1 Answer 1

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The bolded part of "The portion of the chord AE from point A to diameter BC has a length of 7 units" should be a D instead, I think. Here is the diagram:-

enter image description here

(1) The green triangle is similar to the red one.

(2) Using the ratio setup in (1), we can find r.

(3) OX can then be found by Pythagoras theorem.

(4) Using one of the ratios setup in (1) again, you should be able to get EC = 6.32.

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