3 points on a straight line!

Geometry Level 3

The above shows two squares \(ABCD\) and \(EFGH\) with side lengths 10 and 6, respectively. Given that \(A,E,F\) and \(B\) lies on a straight line. And the straight line \(AE\) has a distance of 1.

If \(\vec{AI} = \beta \vec{EI} \), what is the value of \(\beta\)?

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