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The problem presented involves a circular swimming pool, marked with key points, such as ladders at points \(A\) and \(B\), a slide at point \(P\), and two spotlight sources at \(L_1\) and \(L_2\). The objective is to calculate the distance between point \(TS_1\), which is located on the boundary of an illuminated area, and the spotlight source \(L_2\).

### Let's break down the problem and solve it:

1. **Given Data**:
   - The pool has a diameter of 20 meters, making its radius \( r = 10 \) meters.
   - \( P \), the position of the slide, is 4 meters from the center \( O \).
   - The distance between the slide at \( P \) and the spotlight at \( L_2 \) is 20 meters.
   - \( TS_1 \) and \( TS_2 \) represent boundary points still receiving light from \( L_2 \).

2. **Objective**: 
   - Determine the length of the line segment connecting \( TS_1 \) to \( L_2 \).

### To proceed:
- First, we need to analyze the geometric relationships between the various points.
- By knowing the distances, we can apply the **Pythagorean theorem** or use **trigonometric properties** to find the required length.

I'll start calculating the solution.The approximate distance between point \( TS_1 \) and spotlight \( L_2 \) is about **19.60 meters**.

This calculation assumes geometric properties based on the provided distances, particularly the relationship between point \( P \), the pool's center \( O \), and \( L_2 \).

Would you like more details or have any other questions?

Here are some related questions you can explore:
1. How do we derive the distance formula used in this calculation?
2. What geometric properties of circles are used in problems like this?
3. How does the position of \( P \) inside the circle affect other distances?
4. Can we calculate the angle between points \( P \), \( O \), and \( L_2 \)?
5. How would changing the position of \( L_2 \) affect the illuminated area?

**Tip**: Using the Pythagorean theorem is very useful when dealing with distances in circular diagrams, especially when you know two sides of a triangle.

Diberikan sebuah diagram yang menunjukkan sebuah kolam renang berbentuk lingkaran dilengkapi dengan dua buah tangga kolam (titik A dan B) dan sebuah perosotan (titik P). Di bagian tepi kolam dipasang sebuah lampu sorot (L1) dan lampu sorot lainnya diletakkan di belakang daerah perosotan (L2). Diameter dari kolam renang tersebut adalah 20 m. Posisi perosotan (P) dengan lampu sorot (L2) berjarak 20 m. Titik TS1 dan TS2 adalah batas daerah yang masih bisa mendapatkan sinar lampu L2. Tentukan panjang garis yang menghubungkan titik TS1 dengan L2!

Pelajari cara menghitung panjang garis antara titik TS1 dan lampu sorot L2 pada diagram kolam renang berbentuk lingkaran. Masalah ini melibatkan konsep geometri seperti teorema Pythagoras dan formula jarak. Cocok untuk siswa kelas 10-12.

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