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Let's analyze the given information and solve the required tasks step by step.

### Given:
- \( A \) is the center of the circle.
- \( BD \) is a diameter.
- \( m\angle BC = 100^\circ \) (arc \( BC \)).

### Tasks:

#### (a) **Identificar un ángulo central** (Identify a central angle)
- A central angle is an angle whose vertex is at the center of the circle, and its sides pass through two points on the circle.
- The angle \( \angle BAC \) is a central angle because \( A \) is the center, and its sides pass through \( B \) and \( C \).

#### (b) **Identificar un arco mayor** (Identify a major arc)
- A major arc is an arc larger than 180°. Since \( BD \) is the diameter, the circle is divided into two semicircles. The major arc here would be \( BCD \), which is more than 180°.

#### (c) **Identificar un arco menor** (Identify a minor arc)
- A minor arc is less than 180°. The arc \( BC \) is a minor arc since its given measure is 100°, which is less than 180°.

#### (d) **Hallar \( \angle BAC \)** (Find \( \angle BAC \))
- \( \angle BAC \) is a central angle that subtends the arc \( BC \). Therefore, the measure of the central angle \( \angle BAC \) is equal to the measure of the arc it subtends, which is \( 100^\circ \).

#### (e) **Hallar \( m \angle BEC \)** (Find \( m\angle BEC \))
- \( \angle BEC \) is an inscribed angle that subtends the same arc \( BC \) as the central angle \( \angle BAC \). The measure of an inscribed angle is half the measure of the arc it subtends.
- Therefore, \( \angle BEC = \frac{1}{2} \times 100^\circ = 50^\circ \).

### Final Answers:
(a) \( \angle BAC \)  
(b) Arc \( BCD \) (major arc)  
(c) Arc \( BC \) (minor arc)  
(d) \( 100^\circ \)  
(e) \( 50^\circ \)

Would you like further clarification on any of these steps, or additional details?

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Here are 5 related questions to further explore this topic:
1. How do you find the measure of an inscribed angle when it subtends a semicircle?
2. What is the relationship between a diameter and a central angle?
3. How can you calculate the total sum of the angles inside a circle?
4. What is the rule for finding the length of an arc in terms of the circle's radius?
5. How can you prove that an inscribed angle is half of a central angle?

**Tip:** In a circle, the measure of an inscribed angle is always half the measure of the intercepted arc.

En el siguiente círculo, A es el centro, BD es un diámetro y mBC = 100°. Usar esta información para llenar los espacios vacíos.

Solve a geometry problem involving a circle with a diameter BD, an arc BC = 100°, and center A. Identify central and inscribed angles, major and minor arcs, and apply key theorems such as the Central Angle and Inscribed Angle Theorem. Suitable for Grades 9-11.

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