One radian is the angle subtended at …………. By an arc ……………… .

Answer

To answer the question "One radian is the angle subtended at …………. By an arc ………………", we can break it down into steps.

### Step-by-Step Solution:

1. **Understanding Radian Measurement**:
- A radian is a unit of angular measurement. It is defined based on the relationship between the length of an arc and the radius of the circle.

2. **Defining the Circle**:
- Consider a circle with a center point. Let’s denote the radius of the circle as \( R \).

3. **Drawing the Angle**:
- From the center of the circle, draw two radii that create an angle \( \theta \). This angle is what we are trying to define in radians.

4. **Arc Length**:
- The arc length \( L \) is the distance along the circumference of the circle between the two points where the radii intersect the circle.

5. **Relationship Between Angle, Arc Length, and Radius**:
- The relationship is given by the formula:
\[ \theta = \frac{L}{R} \]
- Here, \( \theta \) is in radians, \( L \) is the length of the arc, and \( R \) is the radius of the circle.

6. **Condition for One Radian**:
- For \( \theta \) to be equal to 1 radian, the length of the arc \( L \) must be equal to the radius \( R \):
\[ \theta = 1 \text{ radian} \implies L = R \]

7. **Filling in the Blanks**:
- Therefore, we can fill in the blanks:
- One radian is the angle subtended at **the center of the circle** by an arc **equal in length to the radius of the circle**.

### Final Answer:
One radian is the angle subtended at **the center of the circle** by an arc **equal in length to the radius of the circle**.