Question

The radius of the circle passing through the points \[ (5, 7), \quad (2, -2), \quad (-2, 0) \] is

• A. 2 units
• B. 5 units
• C. 4 units
• D. 3 units

Hint:

To find the radius of a circle passing through three points, use the formula involving the distances between the points and the area of the triangle formed by them.

Answer 1

The Correct Option is B

Step 1: Using the formula for the radius of the circle.
The radius \( R \) of a circle passing through three points \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \) is given by the formula: \[ R = \frac{\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} \cdot \sqrt{(x_2 - x_3)^2 + (y_2 - y_3)^2} \cdot \sqrt{(x_3 - x_1)^2 + (y_3 - y_1)^2}}{2 \times \text{Area of triangle formed by the points}}. \]
Step 2: Applying the formula.
Using the points \( (5, 7) \), \( (2, -2) \), and \( (-2, 0) \), we calculate the radius to be 5 units.

Step 3: Conclusion.
Thus, the radius of the circle is 5 units, which makes option (B) the correct answer.