Directions: Decide whether the data provided in the two statements given under the question is sufficient to answer the question or not. Given option
Wha is the perimeter of the circle?
I. The centre (0,0) of the circle is at a distance of 5 units from the point P (3,4)
II. The images of P with respect to both x-axis and y-axis lie on the circle

Given:

Find the perimeter of the circle.

Statement I: Centre of circle is (0,0) and its distance from point P(3,4) is 5 units.

Statement II: Images of P w.r.t x-axis and y-axis lie on the circle.

Formula used:

Radius = Distance between centre and any point on the circle

Perimeter of circle = \(2\pi r\)

Calculation:

From Statement I:

Distance from (0,0) to (3,4) = \(\sqrt{3^2 + 4^2} = \sqrt{9+16} = \sqrt{25} = 5\)

⇒ Radius = 5

Perimeter = \(2\pi \times 5 = 10\pi\)

Statement I alone is sufficient.

Statement II gives additional points on circle but doesn't give radius directly.

⇒ II alone is not sufficient.

∴ The correct answer is option (1).