python - Finding coordinates of point on line joining two points at certain distance from one of points using shapely

I am new to GIS. The question I am going to ask has been asked before but it didn't solve my purpose. I am only using python and shapely. I need to find the coordinates of a point on a line joining two points at a given distance from one of the points. To help illustrate, I am including the following figure:

In the figure, I need to find the coordinates (lat/lon) values of the red points at a certain distance (say d1*1.01) from the point marked as C. Given are the points C, and P1,P2 and P3 with their coordinates in lat/lon format. How do I do find these values (lat/lon values of the red points) using only python and shapely. I don't want to incorporate Arcpy unless there is no other options.