The probability of the diameter of a circle being the longest chord of he circle is :

Options

A. 1
B. 0
C. `(1)/(2)`
D. cannot be determined

Answer

To find the probability of the diameter of a circle being the longest chord of the circle, we can follow these steps:

### Step 1: Understand the Definitions
- A chord of a circle is a line segment with both endpoints on the circle.
- The diameter is a special type of chord that passes through the center of the circle and is the longest possible chord.

### Step 2: Identify Favorable Outcomes
- The only favorable outcome for our question is the diameter itself, as it is the only chord that can be considered the longest chord of the circle.

### Step 3: Count the Favorable Outcomes
- There is only **1** diameter in a circle. Therefore, the number of favorable outcomes (nf) is **1**.

### Step 4: Count the Total Outcomes
- Since we are only considering the longest chord, there is also only **1** longest chord in the circle, which is the diameter. Therefore, the total number of outcomes (nt) is also **1**.

### Step 5: Calculate the Probability
- The probability (P) of an event is given by the formula:
\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} = \frac{nf}{nt} \]
- Substituting the values we found:
\[ P = \frac{1}{1} = 1 \]

### Conclusion
- The probability of the diameter of a circle being the longest chord of the circle is **1**.

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