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Question
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.
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.
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Solution
The correct option is A Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1
Equal chords are equi-distant from the centre of the circle. Also, a perpendicular from the centre of the circle to the chord is a perpendicular bisector of the chord. Hence, as the mid-points are equi-distant from the center of the circle, the locus of the middle points is a circle with center at the center of the original circle. Hence, statement 1 is true, statement 2 is true and statement 2 is the correct explanation of statement 1.
Equal chords are equi-distant from the centre of the circle. Also, a perpendicular from the centre of the circle to the chord is a perpendicular bisector of the chord. Hence, as the mid-points are equi-distant from the center of the circle, the locus of the middle points is a circle with center at the center of the original circle. Hence, statement 1 is true, statement 2 is true and statement 2 is the correct explanation of statement 1.
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