Final answer:
To calculate the radius of the circle, we use the distance formula between the center point (4,6) and the point on the circle (1,2), resulting in a radius of 5 units.
Step-by-step explanation:
The question asks to find the length of the radius of a circle with a given center and a point that lies on it. To find the radius, we need to calculate the distance between the center of the circle (4,6) and the point (1,2) on the circle's perimeter. This can be done using the distance formula: √((x2 - x1)² + (y2 - y1)²).
Using this formula, we get:
- x2 - x1 = 4 - 1 = 3
- y2 - y1 = 6 - 2 = 4
Plugging these into the distance formula gives us:
√(3² + 4²) = √(9 + 16) = √25 = 5
Therefore, the length of the radius is 5 units, making the correct answer b) 5.