Question

Find the radius of the circle whose centre is at (2, 2) and which passes through the point (6, 5).
1. 8
2. 7
3. 5
4. 2

Answer 1

Correct Answer - Option 3 : 5

Concept:

Let A (x1, y1) and B (x2, y2) be any two points in the XY – plane, then the distance between A and B is given by:\(\rm \left| {AB} \right| = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \)
Calculation:

The center of the circle is at (2, 2). Since, the point (4, 5) lies on the circle, the distance of the center from this point is the radius r of the circle.
Therefore, we obtain

\(\rm r = \sqrt {{{\left( { 6 - 2} \right)}^2} + {{\left( {5 - 2} \right)}^2}} = \sqrt {16 + 9} = \sqrt{25 }=5\)