find the locus of the foot of perpendicular drawn fromthe origin to any chord of the circle S=0 which subtends a right angle at the origin

We are asked to find the locus of the foot of the perpendicular drawn from the origin to any chord of a circle that subtends a right angle at the origin.

### Step-by-Step Solution:

1. **Equation of the Circle:**
Let the equation of the circle be given by \( S = 0 \). Typically, the equation of a circle is of the form:

\[
x^2 + y^2 + 2gx + 2fy + c = 0
\]

But the specific equation of the circle is not provided, so we will proceed with the general case.

2. **Right-Angle Subtended by the Chord:**
The problem states that the chord subtends a right angle at the origin. This means that if the origin is the vertex of the angle, the points where the chord intersects the circle must satisfy the condition that the angle between the vectors from the origin to the endpoints of the chord is \( 90^\circ \).

In terms of vectors, for a chord \( AB \) to subtend a right angle at the origin, we have:

\[
\overrightarrow{OA} \cdot \overrightarrow{OB} = 0
\]

where \( O \) is the origin, and \( A \) and \( B \) are the endpoints of the chord. This condition implies that the vectors \( \overrightarrow{OA} \) and \( \overrightarrow{OB} \) are perpendicular to each other.

3. **Foot of the Perpendicular:**
Let the foot of the perpendicular from the origin to the chord \( AB \) be denoted by \( P \). The foot of the perpendicular is the point on the chord closest to the origin. To find the locus of \( P \), we need to determine the set of all possible positions of \( P \) as the chord \( AB \) moves around the circle.

4. **Geometric Interpretation:**
The key observation is that the chord \( AB \) subtending a right angle at the origin implies that the origin lies on the circle's diameter that is perpendicular to the chord. Since the foot of the perpendicular from the origin to any chord of the circle lies on a straight line perpendicular to the chord, the locus of the foot of the perpendicular is a circle.

5. **Locus of the Foot of the Perpendicular:**
The locus of the foot of the perpendicular from the origin to the chord of the circle that subtends a right angle at the origin is a circle whose radius is half the radius of the given circle.

### Final Answer:
The locus of the foot of the perpendicular drawn from the origin to any chord of the circle that subtends a right angle at the origin is a circle with a radius half of the radius of the given circle, and it is concentric with the given circle.