I've modified the first sketch a little bit.
If the center of the circle has the coordinates $\displaystyle C(x_C, y_C)$ then the point P has the coordinates $\displaystyle P(x_C+u , y_C + v)$
Use the right triangle with the legs u and v and the hypotenuse r . Then
$\displaystyle \color{red}v = r \cdot \sin(q)$ and
$\displaystyle \color{blue}u = r \cdot \cos(q)$
I've modified the 2nd sketch a little bit.
1. Determine the coordinates of S and T. Use the attached sketch.
2. You are supposed to know the formula to calculate the slope of a line which runs through 2 points.
If the points are $\displaystyle P(x_P, y_P)$ and $\displaystyle Q(x_Q, y_Q)$ then the slope, determined by these points, is:
$\displaystyle m_{PQ}=\dfrac{y_Q - y_P}{x_Q - x_P}$