A circle of radius 10 is drawn with the origin as the centre.

i) Check whether each of the points with coordinates (6, 9), (5, 9), (6, 8) is inside, outside or on the circle.

ii) Write the coordinates of 8 points on this circle.

(i) [If the distance between the centre and the point is greater than Radius, then the point is outside the circle.

If the distance between the centre and the point is smaller than Radius, then the point is inside the circle.

If the distance between the centre and the point is equal to Radius, then the point is on the circle.]

Centre of the circle = (0,0)(given)

Radius = 10

The distance between origin and (6,9) = = √117>10

⇒ Point (6,9) is outside the circle.

The distance between origin and (5,9) = = √106>10

⇒ Point (5,9) is outside the circle.

The distance between origin and (6,8) = = √100 = 10

⇒ Point (6,8) is outside the circle.

(ii) Let the coordinates of the point on the circle be (x,y)

Then, distance of it from the origin(center) = 10

⇒ = 10

⇒ = 10

⇒

All the possible solutions of the above equation will be on the circle.

Such 8 points are,(6,8),

(√10,√90),

(√20,√80),

(√30,√70),

(√40,√60),

(√50,√50),

(√60,√40),

(√70,√30).