If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc `PXA cong"arc "PYB`.

Explanation

To prove that arc \( PXA \) is congruent to arc \( PYB \), we will follow these steps:

### Step 1: Understand the Given Information
We have a circle with a chord \( AB \). The perpendicular bisector of the chord \( AB \) intersects the circle at points \( P \) and \( Q \). Let \( M \) be the midpoint of the chord \( AB \).

**Hint:** Identify the key elements in the problem: the circle, the chord, and the perpendicular bisector.

### Step 2: Establish the Properties of the Perpendicular Bisector
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