Question

The line 2x−y+1=0 is tangent to a circle at point (2,5) and the centre of the circle lies on x−2y=4. Then the radius of the circle is ____ units.

A. 3√5
B. 5√3
C. 2√5
D. 5√2

Answer 1

To find the radius of the circle, we need to find the coordinates of the center of the circle. We can do this by solving the system of equations: 2x - y + 1 = 0 and x - 2y = 4. Solving these equations, we get x = 2 and y = 0. Therefore, the center of the circle is (2, 0). The radius of the circle is 5 units.

Step-by-step explanation:

To find the radius of the circle, we need to find the coordinates of the center of the circle. We can do this by solving the system of equations: 2x - y + 1 = 0 and x - 2y = 4. Solving these equations, we get x = 2 and y = 0. Therefore, the center of the circle is (2, 0).

To find the radius, we can use the distance formula between the center of the circle and the point of tangency (2, 5). The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates, we get:

d = sqrt((2 - 2)^2 + (0 - 5)^2) = sqrt(0 + 25) = 5

Therefore, the radius of the circle is 5 units.