Multiple choice

STATEMENT - 1 : The locus of the middle points of equal chords of a circle with centre at O is a circle with centre at O STATEMENT - 2 : The mid point of the equal chords are equidistant from the centre of the circle.

  1. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

  2. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

  3. Statement - 1 is True, Statement - 2 is False

  4. Statement - 1 is False, Statement - 2 is True
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A Correct answer
Explanation

Equal chords in a circle are equidistant from the center. The locus of points equidistant from the center is a circle. Both statements are true and the second explains the first.

AI explanation

The perpendicular distance from the center of a circle to a chord uniquely determines the length of that chord, meaning equal chords are equidistant from the center, making Statement 2 true. The midpoint of any chord is the foot of the perpendicular from the center. The locus of points equidistant from a central point forms a circle centered at that same point, making Statement 1 true. Statement 2 provides the direct logical reason for Statement 1.

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