Given the points $O\left(0, 0\right)$ and $R\left(–5, –12\right)$:

1. What is the equation of the circle centered at point $O$ and passing through point $R$?

   Hint 1(a):

   Determine the radius of the circle.
   $r = 13$

   Hint 2(a):

   Use the general equation of a circle:
   $\left(x − h\right)^{2} + \left(y − k\right)^{2} = r^{2}$

2. What is the measure of the angle formed by $\overline { O R }$ and the positive $x$-axis? Answer in both radians and degrees.

   Hint (b):

   Use a trigonometric function to determine the angle $θ$.

   

3. Graph your circle in part (a) and $x^{2} + y^{2} = 144$ on the same set of axes. Shade the region between the circles.

   Hint (c):

   Create a graph.

4. If we use these circles as a dart board and the dart is certain to hit randomly somewhere within the largest circle, what is the probability of hitting the shaded region?

   Hint (d):

   Determine the area of the shaded area and the total area.