Spiral of right triangles

Geometry Level 5

Let \(A_0 = (-1,0)\), and let \(O\) be the origin \((0,0)\). For each integer \(i \geq 1\), we construct the point \(A_i\) so that \(|A_{i-1}A_i| = |A_{i-1}O|\) and the angle \(\angle OA_{i-1}A_i\) is a right angle. If \(O, A_{i-1}, A_{i+1}\) are not collinear for any value of \(i\), what is the \(x\)-coordinate of \(A_{12}\)?

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