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Q.

Which one of the following statements is true?

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a

 If two circles are equal, then their radii are not equal.

b

Only one line can pass through a single point.

c

There are an infinite number of lines that pass through two distinct points.

d

Two distinct lines cannot have more than one point in common.

answer is C.

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Detailed Solution

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The statement, "Only one line can pass through a single point" is incorrect as through a single point an infinite number of lines can pass.

The statement, "There are an infinite number of lines that pass through two distinct points" is incorrect as, through 2 distinct points, one and only one line can pass which contains both points.

The statement, "If two circles are equal, then their radii are not equal" is incorrect, as when 2 circles are equal, their radii are also equal.

The statement, "Two distinct lines cannot have more than one point in common" is correct because if two lines are different, they cannot intersect at more than one point. In other words, two lines can intersect only once. This is a consequence of the fact that lines in Euclidean geometry are assumed to be perfectly straight and infinitely long.

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