https://file.aiquickdraw.com/mathbot/file/1726193477147cth9axx0.jpg

The problem given in the image involves a circle with center \( O \). The task is to calculate the size of the angle \( \angle BOC \), given that \( \angle ADB = 70^\circ \) and \( \angle AOC = 74^\circ \).

Here’s the breakdown:

1. **Explanation of key parts**:
   - \( O \) is the center of the circle.
   - \( \angle ADB = 70^\circ \) is an inscribed angle.
   - \( \angle AOC = 74^\circ \) is a central angle subtended by the arc \( AC \).
   - We are asked to find the value of \( \angle BOC \).

2. **Understanding the Relationship**:
   - The inscribed angle \( \angle ADB \) subtends the same arc as the central angle \( \angle AOB \).
   - The inscribed angle is always half the central angle subtending the same arc. This means:
     \[
     \angle AOB = 2 \times \angle ADB = 2 \times 70^\circ = 140^\circ
     \]

3. **Finding \( \angle BOC \)**:
   - The total angle around the center \( O \) on a circle is \( 360^\circ \). So:
     \[
     \angle BOC = 360^\circ - (\angle AOB + \angle AOC)
     \]
     Substituting the values:
     \[
     \angle BOC = 360^\circ - (140^\circ + 74^\circ) = 360^\circ - 214^\circ = 146^\circ
     \]

Thus, the measure of \( \angle BOC \) is **146°**.

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Would you like more details on this solution, or have any other questions?

Here are five related questions:
1. How is the relationship between central and inscribed angles derived?
2. What other methods can be used to find angles in a circle geometry problem?
3. How can you prove that the sum of angles around a point is \( 360^\circ \)?
4. If \( \angle AOC \) were increased, how would \( \angle BOC \) change?
5. What are some real-world applications of circle geometry?

**Tip**: Remember that inscribed angles are always half of the central angle subtending the same arc in a circle.

Titik O adalah titik pusat lingkaran. Jika besar LADB = 70°, maka besar LBOC adalah?

Learn how to calculate the angle BOC in a circle where the center is at point O, given that angle ADB is 70°. This problem explores key circle geometry concepts, including the relationship between inscribed and central angles, and the sum of angles around a point. Suitable for Grades 7-9.

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