PQR is a triangle right-angled at P and M is a point on QR such that `P M_|_Q R`. Show that`P M^2=Q M.M R`.

Explanation

To prove that \( PM^2 = QM \cdot MR \) in triangle \( PQR \) where \( P \) is the right angle and \( PM \) is perpendicular to \( QR \), we can follow these steps:

### Step 1: Understand the Configuration
We have triangle \( PQR \) with \( P \) as the right angle. Point \( M \) lies on side \( QR \) such that \( PM \) is perpendicular to \( QR \).

### Step 2: Apply the Pythagorean Theorem
In triangle \( PQR \), since \( P \) is the right angle, we can apply the Pythagorean theorem:
\[
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