Two congruent circles intersect each other at points A and B. Through A any linesegment PAQ is drawn so that P, Q lie on the two circles. Prove that `B P\ =\ B Q`.

Explanation

To prove that \( BP = BQ \) when two congruent circles intersect at points \( A \) and \( B \), and a line segment \( PAQ \) is drawn such that \( P \) and \( Q \) lie on the two circles, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Circles and Points**:
Let the two congruent circles be \( C_1 \) and \( C_2 \), intersecting at points \( A \) and \( B \). Draw the line segment \( PAQ \) such that \( P \) lies on circle \( C_1 \) and \( Q \) lies on circle \( C_2 \).

**Hint**: Visualize the two circles and mark the points of intersection clearly.
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