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Question
The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.
Solution
Radius of the circle = 30 units.
The point O is (0, 0).
Let a intersect the x-axis and b intersect the y-axis.
∴ The point A is (a, 0) and B is (0, b)
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
OA = `sqrt(("a" - 0)^2 + (0 - 0)^2`
30 = `sqrt("a"^2)`
Squaring on both sides
302 = a2
∴ a = 30
The point A is (30, 0)
OB = `sqrt((0 - 0)^2 + ("b" - 0)^2`
= `sqrt(0^2 + "b"^2)`
30 = `sqrt("b"^2)`
Squaring on both sides
302 = b2
∴ b = 30
The point B is (0, 30)
Distance AB = `sqrt((30 - 0)^2 + (0 - 30)^2`
= `sqrt(30^2 + 30^2)`
= `sqrt(900 + 900)`
= `sqrt(1800)`
= `sqrt(2 xx 900)`
= `30sqrt(2)`
∴ Distance between the two points = `30sqrt(2)`
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