Solving when a circle and rotating line collide

I am trying to solve for when a circle and a line rotating about a point will collide:

**Updated:**

http://i273.photobucket.com/albums/j...dog/mathp2.png

I am trying to solve for **T**.

The arrow from **Bo** to **B** represents **Bv** or the velocity of the circle.

The arrow from the bottom line to **P** represents **θv** or the change of the rotating line.

The dashed line and circle represents a possible solution to the problem and I only put it there to help me think through the problem.

Constants:

**L**: length of the rotating line (**CP**)

**C**: point the line rotates around

**Cx**, **Cy**: components of **C**

**Bo**: initial point/location of the circle

**Box**, **Boy**: components of **Bo**

**Bv**: velocity of the circle

**Bvx**, **Bvy**: components of **Bv**

**r**: radius of the circle

**θ**: initial rotation of the rotating line (**CP**)

**θv**: rotational velocity of the rotating line (**CP**)

Variables:

**P**: end point of the rotating line (**CP**) at time **T**

**Px**, **Py**: components of **P**

**N**: normal of the line rotating line (**CP**) at time **T**

**Nx**, **Ny**: components of **N**

**B**: point/location of the circle at time **T**

**Bx**, **By**: components of **B**

**D**: distance from the center of the circle (**B**) to the rotating line (**CP**) at time **T**

**T**: time (from 0 to 1)

In the last equation **t** is confusing and a bad choice for a variable. It simply represents **θ** + **θv** * **T** as stated.

Here is my reasoning:

At the top I have the positions of the endpoint of the rotating line **P** and the center of the circle **B** defined as functions of time **T**. In order to determine the position of the collision, I must find at what time **T** the distance **D** from the center of the circle **B** and the line **CP** is equal to the radius of the circle **r**, or **D** - **r** = 0. The distance from a point to a line can be found by taking the dot product of the normal of the line (**N**) and the point (**B**). Knowing this I simply expand the equation until all the variables are present and I am left with the final equation at the bottom. I re-condensed the equation into terms of **a**, **b**, and **t** hoping it would help me solve the problem. If I can get **t** out of the sine and cosine functions, I would be able to solve the problem.

I can't figure out what to do from here. I have been staring at this for days.

Thanks,

- Mike