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-by-Step Solution:

1. **Identify the Right Triangles**:
- We know that triangle \( PQR \) is right-angled at \( P \). Therefore, we can apply the Pythagorean theorem.
- We also know that \( PM \) is perpendicular to \( QR \), which means triangle \( PMR \) is also a right triangle at \( M \) and triangle \( PMQ \) is right-angled at \( M \).

...