Answer:
It seems like you're describing a geometry problem involving a circle and some points A, B, C, and D. Can you provide more details or clarify what you'd like assistance with?
Step-by-step explanation:
1. **Given information**:
- Point B is located on the circle.
- Angle B = 32°.
- DO is produced to A such that DO = OA.
2. **Understanding the scenario**:
- Since DO is produced to A such that DO = OA, it implies that the radius of the circle is equal to the line segment DO.
3. **Drawing the situation**:
- Draw a circle with center O.
- Place point B on the circle.
- Draw a line segment from point O to point B to represent the radius of the circle.
- Label angle B = 32°.
4. **Analyzing the problem**:
- We know that in a circle, the angle subtended by an arc at the center is double the angle subtended by it at any point on the circumference.
- In other words, angle at the center is twice the angle at the circumference subtended by the same arc.
- So, angle B = 32° means that the angle subtended by arc AB at the center O is 64°.
5. **Finding the unknown**:
- Now, since DO is produced to A such that DO = OA, it means that angle AOD is a straight angle (180°), and angle AOB = 360° - 64° (since the sum of angles in a circle is 360°).
- So, angle AOB = 296°.
6. **Final step**:
- We have now found angle AOB = 296°.
