(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

In the figure given below, find a point P on CD equidistant from points A and B. 

In the given triangle ABC, find a point P equidistant from AB and AC; and also equidistant from B and C. 

Construct a triangle ABC, with AB = 7 cm, BC = 8 cm and ∠ABC = 60°. Locate by construction the point P such that:

1. P is equidistant from B and C.
2. P is equidistant from AB and BC.
3. Measure and record the length of PB.

Describe the locus for questions 1 to 13 given below:
1. The locus of a point at a distant 3 cm from a fixed point. 

Describe the locus of points at a distance 2 cm from a fixed line. 

Describe the locus of the centre of a wheel of a bicycle going straight along a level road.

Describe the locus of the moving end of the minute hand of a clock. 

Describe the locus of a stone dropped from the top of a tower. 

Describe the locus of a runner, running around a circular track and always keeping a distance of 1.5 m from the inner edge. 

Describe the locus of the door handle, as the door opens.

Describe the locus of points inside a circle and equidistant from two fixed points on the circumference of the circle. 

Describe the locus of the centres of all circles passing through two fixed points. 

Describe the locus of a point in rhombus ABCD, so that it is equidistant from

1. AB and BC;
2. B and D.

The speed of sound is 332 metres per second. A gun is fired. Describe the locus of all the people on the earth’s surface, who hear the sound exactly one second later.

Describe the locus of points at distances less than 3 cm from a given point.

Describe the locus of points at distances greater than 4 cm from a given point. 

Describe the locus of points at distances less than or equal to 2.5 cm from a given point. 

Describe the locus of points at distances greater than or equal to 35 mm from a given point. 

Sketch and describe the locus of the vertices of all triangles with a given base and a given altitude. 

In the given figure, obtain all the points equidistant from lines m and n; and 2.5 cm from O.