Find intersection by knowing a point, direction, circle position and radius (2D)

  c++, math

#Problem

Hey I wondered how we can find the intersection between a point with a vector direction, assuming that the point is in the circle.
In Other words, how can I find where the particle will hit the circle circumference when I know the following: Circle position, radius, Particle Position and direction (velocity).

#Implementation

I am currently creating a flight radar, all flights are stored in a Queue and I need to sort the queue based on the time untill the flight leaves the cirlce (Radar Radius)
So I need to return a Point, thus I can just get the distance and calculate the time based on distance and velocity.

diagram of the situation

Source: Windows Questions C++

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