ELMO 2018 Problem 3

Let $A$ be a point in the plane, and $\ell$ a line not passing through $A$ . Evan does not have a straightedge, but instead has a special compass which has the ability to draw a circle through three distinct noncollinear points. (The center of the circle is not marked in this process.) Additionally, Evan can mark the intersections between two objects drawn, and can mark an arbitrary point on a given object or on the plane.

(i) Can Evan construct* the reflection of $A$ over $\ell$ ?

(ii) Can Evan construct the foot of the altitude from $A$ to $\ell$ ?

*To construct a point, Evan must have an algorithm which marks the point in finitely many steps.

Proposed by Zack Chroman