# 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 $A_{12}$?

×

Problem Loading...

Note Loading...

Set Loading...