Given a semicircle with center (0, 0) and radius 1. Draw two lines $d_1$ and $d_2$ parallel with the horizontal axis, and very close together. Then draw the reflection of those 2 lines as they hit the semicircle, and take their intersections $A$. If you move $d_1$ and $d_2$ together while keeping them the same distance apart, the path of $A$ will be a curve.
What is the formula of this curve?