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Question

Describe:

(i) The locus of points at distances less than 3 cm from a given point.

(ii) The locus of points at distances greater than 4 cm from a given point.

(iii) The locus of points at distances less than 2.5 cm from a given point.

(iv) The locus of points at distances greater than or equal to 35 mm cm from a given point.

(v) The locus of the centre of a given circle which rolls around the outside of a second circle and is always touching it.

(vi) The locus of the centres of all circles that are tangent to both the arms of a given angle.

(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.

(viii) The locus of points within a circle that are equidistant from the end points of a given chord.

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Solution

i) The locus is the space inside of the circle whose radius is 3 cm and the centre is the fixed point which is given.

ii) The locus is the space outside of the circle whose radius is 4 cm and centre is the fixed point which is given.

iii) The locus is the space inside the circle with a radius of 2.5 cm and the centre is the given fixed point.

iv) The locus is the space outside and circumference of the circle with a radius of 35 mm and the centre is the given fixed point.

v) The locus is the circumference of the circle concentric with the second circle whose radius is equal to the sum of the radii of the two given circles.

vi) The locus of the centre of all circles whose tangents are the arms of a given angle is the bisector of that angle.

vii) The locus of the mid-points of the chords which are parallel to a given chords is the diameter perpendicular to the given chords.

viii) The locus of the points within a circle which are equidistant from the end points of a given chord is the diameter which is perpendicular bisector of the given chord.


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