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We are given that \( AC \) is the diameter of the circle, with center \( O \), and that \( \angle BOA = 100^\circ \). The goal is to find \( \angle CDB \).

### Step-by-Step Solution:

1. **Understanding the Diagram**:
   - \( AC \) is the diameter, so it subtends a right angle at any point on the circle. Therefore, \( \angle ACB = 90^\circ \).
   - \( O \) is the center of the circle, and \( \angle BOA \) is a central angle.

2. **Properties of the Central Angle**:
   - \( \angle BOA = 100^\circ \) is a central angle, meaning it subtends the arc \( BA \) of the circle.

3. **Relationship Between Central and Inscribed Angles**:
   - The angle subtended by the same arc \( BA \) on the circumference (at point \( D \)) is half of the central angle. This is based on the property that an inscribed angle is half the measure of the central angle subtended by the same arc.
   
   Therefore, 
   \[
   \angle CDB = \frac{1}{2} \times \angle BOA = \frac{1}{2} \times 100^\circ = 50^\circ.
   \]

Thus, the measure of \( \angle CDB \) is **50°**.

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Would you like further clarification or details on any step?

### Related Questions:
1. What is the sum of all angles in a triangle inscribed in a circle?
2. How do you calculate the inscribed angle subtended by a semicircle?
3. Can the diameter of a circle always subtend a right angle?
4. How does the length of an arc relate to the angle subtended at the center of a circle?
5. What is the difference between a central angle and an inscribed angle?

**Tip**: Always remember that any triangle inscribed in a circle with one side as the diameter forms a right triangle!

AC merupakan diameter lingkaran yang berpusat di titik O. Jika besar ∠BOA=100°, maka ∠CDB=

This geometry problem asks you to calculate ∠CDB in a circle where AC is the diameter and ∠BOA = 100°. Using the Central Angle Theorem, we find that ∠CDB is 50°. This problem involves circle theorems and is suitable for students in Grades 9-10.

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