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HALLAR EL DIAMETRO, CON EL TEOREMA DE PITAGORAS. DATOS:  CAT OP 7 CM CAT ADY 14 CM

To solve the problem of finding the diameter \( D \) of the circle using the Pythagorean Theorem, let's analyze the given information:

### Given:
- One side (adjacent or horizontal leg) of the right triangle: 14 cm
- The other side (opposite or vertical leg) of the right triangle: 7 cm

### Problem:
Find the diameter \( D \) of the circle.

### Solution:
In the diagram, it appears that the triangle is inscribed in a semicircle, meaning that the hypotenuse of the right triangle represents the diameter of the circle. Using the Pythagorean Theorem:

\[
D = \sqrt{14^2 + 7^2}
\]

### Steps:
1. Calculate \( 14^2 = 196 \).
2. Calculate \( 7^2 = 49 \).
3. Add the two values: \( 196 + 49 = 245 \).
4. Finally, take the square root of 245 to find \( D \).

\[
D = \sqrt{245} \approx 15.65 \text{ cm}
\]

Thus, the diameter \( D \) is approximately 15.65 cm.

Would you like more details or have any questions?

Here are 8 related questions you might consider:
1. What is the circumference of the circle given the diameter \( D \)?
2. How can we calculate the area of the circle with this diameter?
3. What is the radius of the circle?
4. How would the problem change if the legs of the triangle were different?
5. How can the Pythagorean Theorem be applied in other geometric contexts?
6. How does the concept of similar triangles relate to this problem?
7. What is the significance of the right triangle being inscribed in the semicircle?
8. What are other ways to find the diameter if the circle was not inscribed in the triangle?

**Tip:** When solving geometry problems involving circles and triangles, always consider the relationships between the elements, such as radii, diameters, and the Pythagorean Theorem.

Learn how to find the diameter of a circle using the Pythagorean Theorem with a detailed step-by-step solution. Given triangle sides: 14 cm (adjacent) and 7 cm (opposite). Explore related concepts such as circle geometry and the application of the Pythagorean Theorem.

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