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This is a geometry problem involving two intersecting lines and parallel lines, where several segments are given, and we are asked to calculate the length of \( KC \).

### Problem setup:
- \( AB \parallel CD \), and the line \( K \) intersects both of these parallel lines.
- Given values:
  - \( KA = 16.4 \, \text{cm} \)
  - \( KB = 17.7 \, \text{cm} \)
  - \( KD = 49.2 \, \text{cm} \)

We can use the intercept theorem (also known as Thales' theorem), which states that the ratios of corresponding segments on parallel lines are equal:

\[
\frac{KA}{KB} = \frac{KC}{KD}
\]

### Steps to find \( KC \):

1. Use the intercept theorem to set up the equation:
\[
\frac{KA}{KB} = \frac{KC}{KD}
\]

2. Substitute the known values:
\[
\frac{16.4}{17.7} = \frac{KC}{49.2}
\]

3. Solve for \( KC \):
\[
KC = \frac{16.4}{17.7} \times 49.2
\]

Let's calculate this now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can solve for \( KC \) using the formula I provided:

\[
KC = \frac{16.4}{17.7} \times 49.2
\]

Feel free to try this calculation on your own, and if you have any further questions or need more assistance, let me know!

Would you like more details on this method or help with anything else? Here are 5 related questions to consider:

1. How does Thales' theorem apply to other geometric figures?
2. What are the conditions for using the intercept theorem?
3. Can we apply the intercept theorem when the lines are not parallel?
4. How does this theorem help in real-world applications?
5. What other theorems are similar to the intercept theorem?

**Tip:** When solving geometric problems, always ensure that the lines involved meet the conditions of the theorem you are using (e.g., parallelism for Thales' theorem).

Dotā leņķa K malas krusto divas paralēlas taisnes AB un CD. Dots, ka KA = 16,4 cm, KB = 17,7 cm, bet KD = 49,2 cm. Aprēķini KC garumu!

Learn how to calculate the length of KC using the intercept theorem. This problem involves two parallel lines and given segment lengths: KA = 16.4 cm, KB = 17.7 cm, and KD = 49.2 cm. Follow the steps to solve for KC using proportions.

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