The line joining the foot of perpendicular drawn from a point lying on the circumcircle. Of a triangle to the sides of a triangle is a straight line.

Explanation

To prove that the line joining the feet of the perpendiculars drawn from a point \( P \) on the circumcircle of triangle \( ABC \) to the sides of the triangle is a straight line, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Elements**:
- Let \( ABC \) be a triangle with circumcircle \( \omega \).
- Let \( P \) be a point on the circumcircle \( \omega \).
- Drop perpendiculars from point \( P \) to the sides \( BC, AC, \) and \( AB \), and let the feet of these perpendiculars be \( L, M, \) and \( N \) respectively.
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