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# 10th Class Chapter No 15 - Loci in Maths for ICSE

#### Locus

• Locus is the path traced by a moving point satisfying certain conditions

#### Theorem 1

The locus of a point, which is equidistant from two fixed points (A and B), is the perpendicular bisector of the line segment joining the two fixed points.

#### Theorem 2

The locus of a point, which is equidistant from two intersecting straight lines (AB and CD), is  a pair of straight lines which bisect the angles between the given lines

#### Theorem 3

The locus of a point, in a plane and at a fixed distance from a given fixed point, is the circumference of the circle with the given fixed point as centre and given fixed distance as radius

#### Theorem 4

The locus of a point, which is equidistant from two given parallel lines, is a line parallel to the given lines and midway between them

#### Theorem 5

The locus of a point, which is at a given distance from a given line, is a pair of lines parallel to the given line and at the given distance from it

#### Theorem 6

• The locus of the mid-points of all equal chords in a circle is the circumference of the circle concentric with the given circle and having radius equal to the perpendicular distance of all equal chords from the centre
• Equal chords of a circle are equidistant from its centre

#### Theorem 7

The locus of mid-points of all parallel chords in a circle is the diameter of the circle which is perpendicular to the given parallel chords

#### Theorem 8

The locus of a point equidistant from two concentric circles is the circumference of the circle concentric with the given circles and midway between them
Posted in 10th on July 11 2020 at 07:08 AM

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