Through any given set of four points P,Q,R,S it is possible to draw

Options

A. 1. atmost one circle
B. 2. exactly one circle
C. 3. exactly two circles
D. 4. exactly three circles

Answer

To solve the problem of how many circles can be drawn through any given set of four points P, Q, R, and S, we can follow these steps:

### Step 1: Understand the concept of a circle through points
A circle can be defined by three points. If the three points are not collinear (i.e., they do not all lie on a single straight line), then exactly one circle can be drawn through them.

### Step 2: Analyze the set of four points
Given four points P, Q, R, and S, we need to determine if we can draw a circle through all four points.

### Step 3: Check for collinearity
If all four points are collinear, then no circle can be drawn through them. If any three of the four points are non-collinear, we can draw a circle through those three points. However, the fourth point may or may not lie on that circle.

### Step 4: Conclusion on the number of circles
- If all four points are collinear, then **0 circles** can be drawn.
- If any three points are non-collinear, then **exactly 1 circle** can be drawn through those three points, and the fourth point may not lie on that circle.

Thus, through any given set of four points, it is possible to draw at most **1 circle**.

### Final Answer:
At most 1 circle can be drawn through any given set of four points P, Q, R, and S.

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