Question

The centre of the circle is at the origin and its radius is 10. Which of the following points lies inside the circle?

(a) (6, 8)

(b) (0, 11)

(c) (–10, 0)

(d) (7, 7)

Answer 1

Correct option is (d) (7, 7)

Distance between two points (x₁​, y₁​) and (x₂​, y₂​) can be calculated using the formula \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Distance between the points Centre (0, 0) and (6, 8) = \(\sqrt{(6 - 0)^2 + (8 - 0)^2}\)

\(= \sqrt{100}\)

\(= 10\)

Distance between the points Centre (0, 0) and (0, 11) = \(\sqrt{(0 - 0)^2 + (11 - 0)^2}\)

\(= \sqrt{121}\)

\(= 11\)

Distance between the points Centre (0, 0) and (−10, 0) = \(\sqrt{(-10 -0)^2 + (0 - 0)^2}\)

\(= \sqrt{100}\)

\(= 10\)

Distance between the points Centre (0, 0) and (7, 7) = \(\sqrt{(7 - 0)^2 + (7 - 0)^2}\)

\(= \sqrt{49 + 49}\)

\(= 7\sqrt 2\)

Only the distance between the centre and (7, 7) is less than the radius 10.

Hence, (7, 7) lies inside the circle.