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The question asks for the position of the point \( P(5, 12) \) with respect to the circle given by the equation:

\[
x^2 + y^2 = 16
\]

### Steps to solve:
1. **Equation of the Circle**: The given equation, \( x^2 + y^2 = 16 \), represents a circle with its center at \( (0, 0) \) and a radius \( r = \sqrt{16} = 4 \).

2. **Distance from the Center to Point \( P(5, 12) \)**:
   The distance \( d \) between the center of the circle \( (0, 0) \) and the point \( P(5, 12) \) can be found using the distance formula:
   \[
   d = \sqrt{(5 - 0)^2 + (12 - 0)^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13
   \]

3. **Compare the Distance to the Radius**:
   - The radius of the circle is 4.
   - The distance from the center to \( P(5, 12) \) is 13.

Since the distance \( d = 13 \) is greater than the radius \( r = 4 \), the point \( P(5, 12) \) lies **outside the circle**.

### Conclusion:
The position of the point \( P(5, 12) \) with respect to the circle is **outside**.

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Would you like further details or have any questions?

Here are 5 related questions you might explore:
1. What is the equation of a circle with center \( (h, k) \) and radius \( r \)?
2. How do you find the distance between two points in a plane?
3. How can you check if a point lies inside, on, or outside a circle?
4. What is the general form of the equation of a circle in the coordinate plane?
5. How does the distance formula relate to the Pythagorean Theorem?

**Tip**: For any point \( P(x_1, y_1) \), compare the distance from the center to \( P \) with the circle's radius to determine its relative position.

Kedudukan titik P (5, 12) terhadap lingkaran x^2 + y^2 = 16 adalah...

Determine the position of point P (5, 12) with respect to the circle given by the equation x^2 + y^2 = 16. This problem covers the equation of a circle, using the distance formula, and comparing distances to find if a point is inside, on, or outside the circle. Suitable for students in Grades 9-11.

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