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Question

The radius of a circle with centre at origin is 30 units. If the circle intersects the coordinate axes at ‘a’ and ‘b’ respectively, find the distance between the two points.

  1. 253 units
  2. 302 units
  3. 16 units
  4. 22 units


Solution

The correct option is B 302 units
Radius of the circle = 30 units.
The point O is (0, 0).

Since, a intersect the x-axis and b intersect the y-axis.
∴ The point A is (a, 0) and B is (0, b)

Distance =[(x2x1)2+(y2y1)2]
OA=[(a0)2+(00)2]
30=a2
a=30 units

The point A is (30, 0)

Now, OA=[(00)2+(b0)2]
30=b2
b=30 units

The point B is (0, 30)

Hence, distance between point A and Point B is
AB=[(300)2+(030)2]
AB=(302+302)
AB=302 units

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