Spiral of right triangles

Geometry Level 5

Let A0=(1,0)A_0 = (-1,0), and let OO be the origin (0,0)(0,0). For each integer i1i \geq 1, we construct the point AiA_i so that Ai1Ai=Ai1O|A_{i-1}A_i| = |A_{i-1}O| and the angle OAi1Ai\angle OA_{i-1}A_i is a right angle. If O,Ai1,Ai+1O, A_{i-1}, A_{i+1} are not collinear for any value of ii, what is the xx-coordinate of A12A_{12}?

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