If three equal chords meet at three distinct points on the circle , then the angle between any two chords is ______.

Answer

To solve the problem, we need to determine the angle between any two equal chords that meet at three distinct points on a circle. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Problem**: We have a circle with three equal chords that meet at three distinct points. Let's label these points as A, B, and C. Since the chords are equal, we have AB = AC = BC.

2. **Forming a Triangle**: The points A, B, and C form a triangle. Since all three chords are equal in length, triangle ABC is an equilateral triangle.

3. **Properties of an Equilateral Triangle**: In an equilateral triangle, all sides are equal, and all angles are equal. The sum of the angles in any triangle is 180 degrees.

4. **Calculating the Angles**: Since triangle ABC is equilateral, each angle in the triangle is given by:
\[ \text{Each angle} = \frac{180^\circ}{3} = 60^\circ \]
Therefore, angle ABC, angle BCA, and angle CAB are all equal to 60 degrees.

5. **Conclusion**: The angle between any two chords (for example, chords AB and AC) is equal to 60 degrees.

Thus, the angle between any two chords is **60 degrees**.