Solve equation for intercepting object with a circular motion

Job ID: 32649319

Budget: $30 – $250 USD

So currently I have a 2D space game. In the game I am trying to predict where to shoot projectile objects with constant speed towards a moving object (which also has a constant angular speed) which is moving from a start point to an end point.

Given that the start and end points are on a perfect circle, how would I intercept the moving object that is moving towards the end point?

The object only moves from the start point to the end point once.
Related categories: Mathematics Coding Geometry