Mathematics
P is a moving point and AB is a chord of a circle. If P moves, within this circle, in such a way that it is at equal distances from points A and B. The locus of P is :
a chord perpendicular to chord AB
a chord that bisects the chord AB
a diameter of the circle
the diameter of the circle which is perpendicular to chord AB
Locus
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Answer
Let O be the center of the circle and AB be the chord.
Draw XY, perpendicular bisector of AB.
We know that,
Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the two points.
∴ XY is the locus of point P.
We know that,
Perpendicular to a chord passes through center of the circle.
We know that,
Chord passing through the center is the diameter.
Locus of point P is the diameter of the circle which is perpendicular to chord AB.
Hence, Option 4 is the correct option.
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Related Questions
The locus of the centers of all circles, which are tangents to the arms AB and BC of angle ABC is :
perpendicular bisector of arm AB
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none of these
A point P moves in such a way that it is at a distance less than or equal to 5 cm from a fixed point O. The locus of point P is :
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AB is a line segment and P is a moving point that moves in such a way that it is always equidistant from AB. The locus of point P is the line which :
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AB is a line segment. A point P moves in such a way that the triangle APB is always an isosceles triangle with base AB. The locus of point P is the line which :
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passes through the mid-point of AB.