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?

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.