Geometry Chapter 11

Question 1

The locus of points at a given distance from a given point is

Answer 1

a circle whose center is the given point and whose radius is the given distance

Question 2

The locus of points equidistant from the sides of a given angle

Answer 2

is the bisector of the angle

Question 2

The locus of points equidistant from two given intersecting lines

Answer 2

is the bisectors of the angles formed by the lines

Question 3

A point or points which satisfy two conditions may be found

Answer 3

by drawing the locus for each condition. The required points are the points of intersection of the two loci.

Question 4

The locus of points at a given distance from a given line

Answer 4

is a pair of lines, parallel to the given line and at the given distance from the given line.

Question 4

A locus of points

Answer 4

is the set of points, and only those points, that satisfy given conditions.

Question 6

The locus of points equidistant from two concentric circles

Answer 6

is the circle concentric with the given circles and midway between them

Question 7

The locus of points at a given distance from a given circle whose radius is less than the distance

Answer 7

is a circle, outside the given circle and concentric with it.

(If r=d, the locus also includes the center of the given circle.)

Question 8

The locus of points equidistant from two given points

Answer 8

is the perpendicular bisector of the line segment joining the two points

Question 10

The locus of points equidistant from two given parallel lines

Answer 10

is a line parallel to the two lines and midway between them

Question 11

The locus of points at a given distance from a given circle whose radius is greater than that distance

Answer 11

is a pair of concentric circles, one on either side of the given circle and at the given distance from it.