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# Quick Question

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Hi!! I am having a little trouble with the following question. Could someone help me out?

$$ABCDEFGHI$$ is a regular nonagon with side length $$1$$. Let $$M$$ be the midpoint of $$\overline{EF}$$. $$J$$ is a point outside the nonagon such that $$AJ=2$$ and $$\overline{AJ} \perp \overline{AM}$$. Find all possible values of the product
$AJ\cdot BJ\cdot CJ\cdot DJ\cdot EJ\cdot FJ\cdot GJ\cdot HJ\cdot IJ$

Thanks!

Jan 3, 2024

#1
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Turns out there was an error in the question, the nonagon should be inscribed in a circle of radius 1 instead of having a side length of 1. I'm still not sure how to solve it though.

Jan 3, 2024
#2
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Turns out there was an error in the question, the nonagon should be inscribed in a circle of radius 1 instead of having a side length of 1. Also, AJ=1.  I'm still not sure how to solve it though.

Jan 3, 2024
edited by ElemetraryQuestions  Jan 3, 2024
edited by ElemetraryQuestions  Jan 3, 2024
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Unfortunately, your 'elemetary' question is a little too difficult for regular homework helpers. However, the answer is $$\sqrt{481}$$ if CPhill is interested...

Jan 3, 2024
edited by Holtran  Jan 3, 2024