Mathematics
The locus of a point equidistant from two concentric circles is:
a circle concentric with the given circles and inside the smaller circle.
a circle concentric with the given circles and outside the larger circle.
a circle concentric with the given circles and midway between them.
the common centre of the two circles.
Answer
For concentric circles, every point’s distance from each circle is measured along the same radial direction because the centre is common.
A point that is equidistant from both circles must lie at a radius that is exactly midway between the two radii.
Hence, option 3 is the correct option.
Related Questions
A point P moves such that its distance from a fixed line AB is always the same. What is the relation between AB and the path traveled by P ?
It is a set of two lines perpendicular to AB.
It is a set of two lines parallel to AB drawn on either side at equal distance from it.
It is a set of two concentric circles.
It is a set of two intersecting lines with AB bisecting the angle between them.
A point P moves so that its perpendicular distance from two given parallel lines AB and CD are equal. Then, the locus of the point P is:
a line l anywhere in between AB and CD and parallel to them.
a line l perpendicular to both AB and CD.
a line l in the midway of AB and CD and parallel to them.
none of these
The locus of a point which is equidistant from a given circle consists of:
a pair of circles concentric with the given circle.
a circle concentric with the given circle and inside it.
a circle concentric with the given circle and outside it.
a pair of lines parallel to each other on either side of the centre.
A and B are two fixed points in a plane. Then, the locus of a point P which moves in such a way that PA2 + PB2 = AB2, is:
a square with AB as one of its sides.
a rectangle with AB as one of its sides.
a rhombus with AB as one of its diagonal.
the circumference of a circle with AB as its diameter.