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
2 Likes
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.
Answered By
1 Like
Related Questions
Use ruler and compasses only for this question.
(i) Construct △ABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.
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
perpendicular bisector of arm BC
bisector of angle ABC
none of these
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 :
is parallel to AB
is perpendicular to AB
is perpendicular bisector of AB
passes through the mid-point of AB.
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 :
is parallel to AB and through point P.
is perpendicular to AB through point P.
is perpendicular bisector of AB.
passes through the mid-point of AB.