In the figure, `M` is the midpoint of `QR`. `/_PRQ=90^(@)`. Prove that `PQ^(2)=4PM^(2)-3PR^(2)`

Explanation

To prove that \( PQ^2 = 4PM^2 - 3PR^2 \) given that \( M \) is the midpoint of \( QR \) and \( \angle PRQ = 90^\circ \), we will follow these steps:

### Step 1: Identify the triangles
Since \( M \) is the midpoint of \( QR \), we have \( RM = MQ \). We also know that \( \angle PRQ = 90^\circ \), which allows us to apply the Pythagorean theorem in triangle \( PRQ \).

### Step 2: Apply the Pythagorean theorem to triangle \( PRQ \)
Using the Pythagorean theorem:
\[
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