Localizing a point in a circle by 2 points on the circumference

[fenpark15]

I'm looking to find the proper formulas and/or Matlab code to localize a point within a circle given 2 points on the circumference. The points will be acquired by an image panel that rotates about a fixed axis. The hitch is that I am using flat image panels that are tangent to the circle at their center. I would like to measure the offset of a small spherical object from the center of the panel at 2 different positions on the circumference, extend a vector normal to the image panel from where that object appears on the images, and locate the point where the two vectors intersect (the position of the object within the circle). How can I go about doing this? Your help is much appreciated!

 

[fenpark15]

Let me rephrase this request. I'm not looking for anyone to do it for me, I'm just looking for insights or tips. I know that I will need to go about creating a vector or line segment to represent the panel, construct a normal vector from the surface of the panel at a specified point (perhaps by solving to make the dot product=0?), and do the math to find the intersection of 2 such vectors. I'm still looking at a blank page for my methods and I'm wondering if I should tackle this using polar or cartesian coordinates, wondering how to map the position and orientation of the panel to the circle and/or its center, and if there's any nice Matlab function that might take care of more than 1 step at a time for me. Known parameters are the position of the panel, its angle (always tangent to the circle from its center) and the radius to the center.