Drawing an inscribed circle bounded between two arcs and a line

This is a fun problem which requires a little bit of algebra to analyze it to find the center of the inscribed circle. If the arcs of original circles is a then the center of the circle is at (a/2,3a/8). As should be evident from the figure that I used eight circles to achieve that division and than used 3 times of that to get the length 3/8a. After that I used the vector function to place that point on the perpendicular bisector.