Prove that all the chords of a circle through a given point within it, the least is one which is bisected at that point.

Explanation

To prove that among all the chords of a circle passing through a given point within it, the shortest chord is the one that is bisected at that point, we can follow these steps:

### Step-by-Step Solution:

1. **Draw the Circle and Identify Points:**
- Let \( O \) be the center of the circle and \( P \) be a point inside the circle. Draw a circle with center \( O \) and radius \( r \).

2. **Draw Chords Through Point \( P \):**
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