P, Q and R are the points so that PR = 3 cm, QR = 5 cm and PQ = 8 cm. The number of circles passing through the points P,Q and R is:

Options

A. 3
B. 2
C. 1
D. 0

Answer

To solve the problem of finding the number of circles that can pass through the points P, Q, and R, we can follow these steps:

### Step 1: Identify the lengths given in the problem
We have the following lengths:
- PR = 3 cm
- QR = 5 cm
- PQ = 8 cm

### Step 2: Check the relationship between the lengths
We need to check if the points P, Q, and R can form a triangle. For three points to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check:
- PR + QR = 3 cm + 5 cm = 8 cm
- PQ = 8 cm

Since PR + QR = PQ, this means that the points P, Q, and R are collinear.

### Step 3: Conclude about the collinearity of points
Since the points are collinear, they lie on the same straight line.

### Step 4: Determine the number of circles that can pass through collinear points
A circle cannot pass through three collinear points. Therefore, the number of circles that can pass through points P, Q, and R is zero.

### Final Answer
The number of circles passing through the points P, Q, and R is **0**.

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