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Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :
  • a)
    1
  • b)
    √2
  • c)
    2√2
  • d)
    2
Correct answer is option 'D'. Can you explain this answer?
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Let's consider the equation of the first circle centered at (0, 1) with radius r:

(x - 0)^2 + (y - 1)^2 = r^2
x^2 + (y - 1)^2 = r^2

Similarly, the equation of the second circle also centered at (0, 1) with radius r:

(x - 0)^2 + (y - 1)^2 = r^2
x^2 + (y - 1)^2 = r^2

Since the two circles are intersecting at (0, 1), we can substitute these coordinates into the equations:

For the first circle:
0^2 + (1 - 1)^2 = r^2
0 + 0 = r^2
r^2 = 0
r = 0

For the second circle:
0^2 + (1 - 1)^2 = r^2
0 + 0 = r^2
r^2 = 0
r = 0

Therefore, both circles have a radius of 0, which means they are actually the same point at (0, 1).
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Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :a)1b)√2c)2√2d)2Correct answer is option 'D'. Can you explain this answer?
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