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.