Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा १० आईसीएसई chapter 14 - Locus [Latest edition]

Describe completely the locus of a point in the following case:

Midpoint of radii of a circle. 

Describe completely the locus of a point in the following case:

Centre of a ball, rolling along a straight line on a level floor. 

Describe completely the locus of a point in the following case:

Point in a plane equidistant from a given line. 

Describe completely the locus of a point in the following case:

Point in a plane, at a constant distance of 5 cm from a fixed point (in the plane).

Describe completely the locus of a point in the following case:

Centre of a circle of varying radius and touching the two arms of ∠ ABC. 

Describe completely the locus of a point in the following case:

Centre of a circle of varying radius and touching a fixed circle, centre O, at a fixed point A on it.

Describe completely the locus of a point in the following case:

Centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O. 

Draw and describe the locus in the following case:

The locus of points at a distance of 2.5 cm from a fixed line.

Describe the locus of vertices of all isosceles triangles having a common base.

Draw and describe the locus in the following case:

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

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

Draw and describe the locus in the following case:

The locus of a point in rhombus ABCD which is equidistant from AB and AD.

Draw and describe the locus in the following case:

The locus of a point in the rhombus ABCD which is equidistant from the point  A and C.

AB is a fixed line. State the locus of the point P so that ∠APB = 90°. 

A, B are fixed points. State the locus of P so that ∠APB = 60°.

P is a fixed point, and a point Q moves such that the distance PQ is constant. What is the locus of the path traced out by the point Q?

A point P moves so that its perpendicular distances from two given lines AB and CD are equal. State the locus of the point P.

A point moves such that its distance from a fixed line AB is always the same. What is the relation between AB and the path travelled by P?

Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.

1. Construct a triangle ABC in which BC = 6 cm, AB = 9 cm, and ∠ABC = 60°.
2. Construct the locus of all points, inside A ABC, which are equidistant from B and C.
3. Construct the locus of the vertices of the triangles with BC as base, which are equal in area to ΔABC.
4. Mark the point Q in your construction which would make A QBC equal in area to A ABC and isosceles.
5. Measure and record the length of CQ.

Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords, AB and AC, of the circle of length 6 cm and 5 cm respectively.

1. Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction.
2. Construct the locus of points, inside the circle, that are equidistant from AB and AC.

Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, <B = 60°, AD = 5 cm and D is equidistant from AB and BC. Measure CD.

By using ruler and compass only, construct an isosceles triangle ABC in which BC = 5 cm, AB = AC and ∠BAC = 90°. Locate the point P such that 

1. P is equidistant from the sides BC and AC. 
2. P is equidistant from the point B and C.

Without using set squares or a protractor, construct:

1. Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
2. Draw the locus of a point which moves so that it is always 2.5 cm from B.
3. Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
4. Mark the point of intersection of the loci with the letter P and measure PC.

Without using set square or protractor, construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Measure ABC. Find the point R on AD such that RB = RC. Measure the length of AR.

Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD. 

Use ruler and compasses only for this question:

1. Construct ΔABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
2. Construct the locus of points inside the triangle that are equidistant from BA and BC.
3. Construct the locus of points inside the triangle which are equidistant from B and C.
4. Mark the point P which is equidistant from AB, BC, and also equidistant from B and C. Measure and record the length of PB.

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.

Use ruler and compass for this question. Construct a circle of radius 4.5 cm. Draw a chord AB = 6 cm.

1. Find the locus of points equidistant from A and B. Mark the point where it meets the circle as D. 
2. Join AD and find the locus of points which are equidistant from AD and AB. Mark the point where it meets the circle as C.
3. Join BC and CD. Measure and write down the length of side CD of the quadrilateral ABCD.

Using ruler and a compass only construct a semi-circle with diameter BC = 7cm. Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ∠ADC and write it down.

Use ruler and compass to answer this question. Construct ∠ABC = 90°, where AB = 6 cm, BC = 8 cm.

1. Construct the locus of points equidistant from B and C.
2. Construct the locus of points equidistant from A and B.
3. Mark the point which satisfies both the conditions (a) and (b) as 0. Construct the locus of points keeping a fixed distance OA from the fixed point 0.
4. Construct the locus of points which are equidistant from BA and BC.

The circumcentre of a triangle is the point which is ______.

By using ruler and compass only, construct a quadrilateral ABCD in which AB = 6.5 cm, AD = 2 cm and ∠DAB = 75°. C is equidistant from the sides AB and AD, also C is equidistant from the points A and B.

Without using set square or protractor, construct the parallelogram ABCD in which AB = 5.1 cm, the diagonals AC = 5.6 cm and the diagonal BD = 7 cm. Locate the point P on DC, which is equidistant from AB and BС.

AB and CD are two intersecting lines. Find the position of a point which is at a distance of 2 cm from AB and 1.6 cm from CD.

Draw a line segment AB of length 12 cm. Mark M, the midpoint of AB. Draw and describe the locus of a point which is

1. at a distance of 3 cm from AВ. 
2. at a distance of 5 cm from the point М. 

Mark the points P, Q, R, S which satisfy both the above conditions. What kind of quadrilateral is PQRS? Compute the area of the quadrilateral PQRS.

Draw a line segment AB of length 7 cm. Construct the locus of a point P such that area of triangle PAB is 14 cm².

A point P is allowed to travel in space. State the locus of P so that it always remains at a constant distance from a fixed point C.

Draw a straight line AB of length 8 cm. Draw the locus of all points which are equidistant from A and B. Prove your statement.

Using ruler and compass only:

1. Construct a triangle ABC with BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm. 
2. In the above figure, draw a circle with BC as diameter. Find a point ‘P’ on the circumference of the circle which is equidistant from AB and BC. 
3. Measure ∠BCP.