Question

The radius of the circle with centre at the origin is 10 units. Write the coordinates of the point where the circle intersects the axes. Find the distance between any two of such points?

Answer 1

THE POINTS OF INTERSECTION ARE (10,0),(0,10),(-10,0) & (0,-10).
THE DISTANCE BETWEEN ANY TWO OF THESE POINTS IS 
SQUARE OF DISTANCE =10^2 + 10^2
                                      =100 + 100  
                                        =200
THEREFORE DISTANCE = √(200)
                                      =√(5 * 5 * 2 * 2 * 2)
                                      = 10√2
 DISTANCE BETWEEN ANY TWO POINTS WILL BE 10√2 UNITS. 

Answer 2

As the centre lies at (0, 0) and the radius is 10 units

The concyclic points are (10, 0), (0, 10), (0, -10) and (-10, 0)

The distance between two points = $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Distance between (10,0) and (0,10) is

$\sqrt{(0-10)^2 + (10-0)^2}$

$\sqrt{100+ 100} = \sqrt{200} = 10 \sqrt{2}$