Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 16 - Loci (Locus and Its Constructions) [Latest edition]

P is a point on perpendicular bisector of side BC of △ABC, then ______.

P is a point on bisector of angle A of △ABC. Then:

The perpendicular bisector of side AB and bisector of angle ∠A of  △ABC meet at point P. Then:

Using the information in the given diagram, state if:

Bisector of ∠B of △ABC intersects side AC at point P, then point P is ______.

Given: PQ is perpendicular bisector of side AB of the triangle ABC. 

Prove: Q is equidistant from A and B.

Given: CP is bisector of angle C of ΔABC. 

Prove: P is equidistant from AC and BC. 

Given: AX bisects angle BAC and PQ is perpendicular bisector of AC which meets AX at point Y. 

 
Prove:

1. X is equidistant from AB and AC.
2. Y is equidistant from A and C. 

Construct a triangle ABC, in which AB = 4.2 cm, BC = 6.3 cm and AC = 5 cm. Draw perpendicular bisector of BC which meets AC at point D. Prove that D is equidistant from B and C. 

In each of the given figures; PA = PB and QA = QB. 

i.
ii.

Prove, in each case, that PQ (produce, if required) is perpendicular bisector of AB. Hence, state the locus of the points equidistant from two given fixed points.

Construct a triangle ABC in which angle ABC = 75°, AB = 5 cm and BC = 6.4 cm. Draw perpendicular bisector of side BC and also the bisector of angle ACB. If these bisectors intersect each other at point P; prove that P is equidistant from B and C; and also from AC and BC. 

In parallelogram ABCD, side AB is greater than side BC and P is a point in AC such that PB bisects angle B. Prove that P is equidistant from AB and BC. 

In triangle LMN, bisectors of interior angles at L and N intersect each other at point A. Prove that:

1. Point A is equidistant from all the three sides of the triangle.
2. AM bisects angle LMN. 

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 which 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.

The locus of the centres of all the circles, which are tangents to the arms AB and BC of angle ABC is ______.

P is a moving point and AB is a chord of a circle. If P moves, within this circle, in such a way that it is at equal distances from points A and B. The locus of P is ______.

AB is a line segment. A point P moves in such a way that the triangle APB is always an isosceles triangle with base AB. The locus of point P is the line which ______.

AB is a line segment and P is a moving point that moves in such a way that it is always equidistant from AB. The locus of point P is the line which ______.

A point P moves in such a way that it is at a distance less than or equal to 5 cm from a fixed point O. The locus of point P is ______.

Describe the locus of points at distances less than 3 cm from a given 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 vertices of all isosceles triangles having a common base.

Describe the locus of a point P, so that:

AB² = AP² + BP²,

where A and B are 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.

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. 

Describe the locus of the centre of a given circle which rolls around the outside of a second circle and is always touching it.

Describe the locus of the centres of all circles that are tangent to both the arms of a given angle.  

Describe the locus of the mid-points of all chords parallel to a given chord of a circle. 

Describe the locus of points within a circle that are equidistant from the end points of a given chord. 

A straight line AB is 8 cm long. Draw and describe the locus of a point which is:

1. always 4 cm from the line AB.
2. equidistant from A and B.
   Mark the two points X and Y, which are 4 cm from AB and equidistant from A and B. Describe the figure AXBY.

The locus of a point which is equidistant from two non-parallel lines AB and CD is ______.

Three isosceles triangles PBC, QBC and RBC are on the same base, then ______.

Locus of the centres of the circles passing through two fixed points A and B is ______.

A point is equidistant from the sides of an obtuse angle triangle. The point is called ______.

In △ABC, point P moves such that it remains at a fixed distance (i.e. radius) of 2.8 cm from vertex B. The locus of point P is ______.

Draw an ∠ABC = 60°, having AB = 4.6 cm and BC = 5 cm. Find a point P equidistant from AB and BC; and also equidistant from A and B. 

On a graph paper, draw the lines x = 3 and y = –5. Now, on the same graph paper, draw the locus of the point which is equidistant from the given lines.

On a graph paper, draw the line x = 6. Now, on the same graph paper, draw the locus of the point which moves in such a way that its distantce from the given line is always equal to 3 units 

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

Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB. 

Construct a triangle BCP given BC = 5 cm, BP = 4 cm and ∠PBC = 45°.

1. Complete the rectangle ABCD such that:
   1. P is equidistant from AB and BC.
   2. P is equidistant from C and D.
2. Measure and record the length of AB. 

Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.

1. Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
2. Construct the locus of points at a distance of 3.5 cm from A.
3. Construct the locus of points equidistant from AC and BC.
4. Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.