https://file.aiquickdraw.com/mathbot/file/1724732560638ctdefu86.jpg

a. Tentukan garis yang menyinggung matahari dan bulan (lingkaran 1 dan titik)
b. Tentukan garis yang menyinggung bumi dan bulan (lingkaran 2 dan titik)

To solve the problem, let's analyze the image and tackle the questions:

### Step-by-Step Solution

1. **Identify the Elements:**
   - The image shows three circles labeled as **Matahari (Sun)**, **Bulan (Moon)**, and **Bumi (Earth)**.
   - We need to determine the tangent lines that:
     - Touch both the Sun and the Moon.
     - Touch both the Earth and the Moon.

### Part (a) - Tangent Line Between Matahari and Bulan

- **Matahari**: This is the larger circle on the left.
- **Bulan**: This is the smaller circle near the middle.

For the tangent line between the Sun and the Moon:
- The tangent line will touch both circles at a single point without crossing into the interior of either circle.
- The equation of the tangent line can be found by using the general tangent formula for two circles or by geometric construction.

### Part (b) - Tangent Line Between Bumi and Bulan

- **Bumi**: This is the smaller circle on the right.
- **Bulan**: The same circle as before.

For the tangent line between the Earth and the Moon:
- Similar to the first case, we look for a line that touches both circles externally at exactly one point on each circle.

### Tangent Line Formula

For two circles with centers \((x_1, y_1)\), \((x_2, y_2)\) and radii \(r_1\), \(r_2\), the equation of the tangent line can be derived using the following method:
1. **External Tangents**: The lines will not intersect the line connecting the centers of the circles.
2. **Use Geometry**: Draw radii from the centers to the points of tangency, and solve using the point-slope form of the line equation.

### Implementation

To derive the equations of these tangent lines, the following information is needed:
- The centers \((x, y)\) and radii \(r\) of the circles, which can be approximated from the graph.
- The specific coordinates of the points of tangency can then be calculated.

However, since the graph is an image and precise coordinates aren't given directly, a geometric construction approach using the properties of tangents or a visual approximation would be necessary.

Would you like a detailed geometric construction of these lines based on the approximation, or do you have the exact coordinates for a more precise calculation?

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### Relative Questions:
1. How do you calculate the tangent line for two given circles using their centers and radii?
2. What are external tangents, and how are they different from internal tangents in circle geometry?
3. How can you determine the slope of the tangent line given two points?
4. What is the geometric significance of the tangent line in relation to the radii of the circles?
5. Can tangent lines exist if one circle is entirely inside another?

### Tip

Explore how to determine tangent lines between the Sun, Moon, and Earth in circle geometry. This problem involves identifying tangent points and using geometric construction methods to find tangent line equations. Suitable for high school students studying circle geometry and tangent line properties.

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