Mathematics
Assertion (A) : The locus of the mid-points of all equal chords in a circle is the circumference of the circle concentric with the given circle and having radius equal to the distance of equal chords from the center.
Reason (R) : Locus of all points at a fixed distance from a fixed point is a circle with the fixed point as center and fixed distance as radius.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Locus
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Answer
We know that,
The locus of the mid-points of all equal chords in a circle is the circumference of the circle concentric with the given circle and having radius equal to the distance of equal chords from the center.
Locus of all points at a fixed distance from a fixed point is a circle with the fixed point as center and fixed distance as radius.
∴ Assertion (A) and Reason (R) are true.
Hence, Option 3 is the correct option.
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