A circle radius $320$ is tangent to the inside of a circle radius $1000$. The smaller circle is tangent to a diameter of the larger circle at a point $P$. How far is the point $P$ from the outside of the larger circle?
1. Let \( O_1 \) be the center of the larger circle with radius \( 1000 \), and \( O_2 \) be the center of the smaller circle with radius \( 320 \). The smaller circle is tangent to the inside of the larger circle and to a diameter of the larger circle at point \( P \).

2. Since the smaller circle is tangent to the diameter of the larger circle at point \( P \), the distance from \( O_2 \) to \( P \) is equal to the radius of the smaller circle, which is \( 320 \).

3. The distance between the centers of the two circles, \( O_1 \) and \( O_2 \), is the difference in their radii, which is \( 1000 - 320 = 680 \).

4. We need to find the distance from point \( P \) to the outside of the larger circle. To do this, we first find the distance from \( O_1 \) to \( P \).

5. Consider the right triangle \( O_1O_2P \). The hypotenuse \( O_1O_2 \) is \( 680 \), and one leg \( O_2P \) is \( 320 \). We need to find the other leg \( O_1P \).

6. Using the Pythagorean theorem:
   \[
   O_1P = \sqrt{O_1O_2^2 - O_2P^2} = \sqrt{680^2 - 320^2}
   \]
   \[
   O_1P = \sqrt{462400 - 102400} = \sqrt{360000} = 600
   \]

7. The distance from point \( P \) to the outside of the larger circle is the radius of the larger circle minus \( O_1P \):
   \[
   1000 - 600 = 400
   \]

Conclusion:
\[
\boxed{400}
\]