Draw a new line perpendicular to another known line and find crossing point of new line and the boundary of the region

Hello,

I have a reference image that has 5 regions. For each region, I have calculated the minimum distance between its centroid and boundary. I have then drawn a line between each centroid and its corresponding closest pixel. The image is attached for your reference.

I want to draw a line (starting from the centroid of each region) perpendicular to the reference line and then find the crossing point of the perpendicular line on the boundary of each region.

Any help would be highly appreciated.

Thanks, Syed