Mathematics
Locus of the centers of the circles passing through two fixed points A and B is :
a line parallel to line segment AB.
the bisector of the line segment AB.
perpendicular to line segment AB.
perpendicular bisector of line segment AB.
Answer
Let O and O' be the center of the circles, passing through points AB.
Steps of construction :
Join AB.
Draw a perpendicular from O to AB and O' to AB.
We know that,
Perpendicular from center to chord bisects it.
Since, both perpendiculars bisects AB.
∴ OO' is a straight line perpendicular to AB and bisecting it.
Hence, Option 4 is the correct option.
Related Questions
The locus of point which is equidistant from two non-parallel lines AB and CD is :
perpendicular to AB.
perpendicular to CD.
bisector of angle between AB and CD.
perpendicular bisector of CD.
Three isosceles triangles PBC, QBC and RBC are on the same base, then :
P, Q and R are collinear.
△PQR is isosceles triangle.
Q lies on the circumference of a circle with BC as diameter.
Q is mid-point of line segment PR.
A point is equidistant from the sides of an obtuse angle triangle. The point is called :
circumcenter of the triangle.
incenter of the triangle.
centroid of the triangle.
orthocenter of the triangle.
ABC is a triangle. Point P moves with vertex B as center and radius 2.8 cm. The locus of point P is :
bisector of angle ABC.
a line parallel to BC and at a distance of 2.8 cm from it.
circle with center at point B and radius = 2.8 cm.
perpendicular bisector of BC.