Which of the following points lies outside the circle with center (0,0) and radius 5 ?A.(4.1, 1)B.(4, 2)C.(3.8, 3)D.(2, 5)

To determine which point lies outside the circle, we can use the equation of a circle, which is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius. In this case, the center is at (0,0) and the radius is 5.

Let's calculate the distance from the center to each point:

A. (4.1, 1) The distance is sqrt((4.1-0)² + (1-0)²) = sqrt(16.81 + 1) = sqrt(17.81) = 4.22 (approximately)

B. (4, 2) The distance is sqrt((4-0)² + (2-0)²) = sqrt(16 + 4) = sqrt(20) = 4.47 (approximately)

C. (3.8, 3) The distance is sqrt((3.8-0)² + (3-0)²) = sqrt(14.44 + 9) = sqrt(23.44) = 4.84 (approximately)

D. (2, 5) The distance is sqrt((2-0)² + (5-0)²) = sqrt(4 + 25) = sqrt(29) = 5.39 (approximately)

So, the point that lies outside the circle is D. (2, 5) because its distance to the center is greater than the radius of the circle.