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The question asks to determine the value of ∠BEC, given that ∠BOC = 90°. Let's analyze the geometry involved:

### Step-by-step approach:
1. **∠BOC as the central angle**: 
   - In the diagram, point **O** is the center of the circle, and **B**, **O**, and **C** are collinear forming a central angle ∠BOC. This central angle is given as 90°.
   
2. **Relationship between central and inscribed angles**:
   - The inscribed angle ∠BEC subtended by the same arc **BC** as the central angle ∠BOC is half of the central angle.
   
   \[
   \text{Inscribed Angle } ∠BEC = \frac{1}{2} × ∠BOC
   \]
   
   Substituting the given value:
   
   \[
   ∠BEC = \frac{1}{2} × 90° = 45°
   \]

Thus, the value of ∠BEC is **45°**.

### Final Answer:
The correct answer is **45°**.

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Would you like further details or have any questions on this solution?

Here are five related questions to expand this topic:

1. How is the inscribed angle theorem derived?
2. What is the difference between a central and an inscribed angle in a circle?
3. How can we calculate angles in a cyclic quadrilateral?
4. What is the general relationship between a central angle and any arc it subtends?
5. How would the problem change if ∠BOC were different from 90°?

**Tip**: Remember that any angle inscribed in a semicircle (with a diameter as the subtended arc) is always a right angle (90°).

Diketahui besar sudut BOC = 90°, besar sudut BEC = ....

In this geometry problem, you will learn how to calculate the inscribed angle BEC in a circle, knowing that the central angle BOC is 90°. This question explores the relationship between central and inscribed angles. Suitable for Grades 8-10.

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