Question: User: 8
106°
A circle with a chord/segment line from the lower-left interior point to the upper-right point on the circle, and a radius-like line from the upper-right point to the lower-left interior point; the angle marked 106° is inside the circle near the center-right. position_hint = center
1. **Problem Statement:**
We have a circle with a chord and a radius forming an angle of $106^\circ$ inside the circle near the center-right.
2. **Understanding the Problem:**
The angle of $106^\circ$ is formed between a chord and a radius inside the circle.
3. **Key Formula:**
The angle between a chord and a radius at the point where the radius meets the circle is related to the inscribed angle subtended by the chord.
4. **Step-by-step Solution:**
- The angle between the chord and the radius is given as $106^\circ$.
- Since the radius and chord meet at the circle, the angle between them is the angle formed at the circumference.
- The central angle subtended by the chord is twice the inscribed angle.
5. **Calculations:**
- Let the inscribed angle be $\theta$.
- Then the central angle $= 2\theta$.
- Given the angle between chord and radius is $106^\circ$, this is the inscribed angle $\theta$.
- So, the central angle $= 2 \times 106^\circ = 212^\circ$.
6. **Interpretation:**
- The central angle subtended by the chord is $212^\circ$.
- This means the chord subtends a major arc of $212^\circ$ and a minor arc of $360^\circ - 212^\circ = 148^\circ$.
**Final answer:**
The central angle subtended by the chord is $$212^\circ$$.