Locus of the Points Equidistant From Two Given Points

Q.

A circle is inscribed in a ΔABC having AB= 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be

1. AD = 3cm, BE = 7cm, CF = 5cm

2. AD = 5cm, BE = 9cm, CF = 4cm

3. AD = 2cm, BE = 6cm, CF = 7cm

4. AD = 4cm, BE = 6cm, CF = 8cm

Q. Construct a triangle PQR with sides QR = 7 cm, PQ = 6 cm and $\angle$PQR = 60º. Then construct another triangle whose sides are $\frac{3}{5}$ of the corresponiding sides of ∆PQR. [CBSE 2014, 2015]

Q.

The lengths of ALL perpendicular line segments between two parallel lines are equal.

1. True

2. False

Q. Question 142
Two sticks each of length 7 cm are crossing each other such that they bisect each other at right angles. What shape is formed by joining their end points? Give reason.

Q. The locus of all the points equidistant from two points is the ________ of the line segment joining the two points.

1. None of the above
2. any line
3. parallel Lines
4. perpendicular bisector

Q.

Draw a line segment of length $9.5cm$ and construct its perpendicular bisector.

Q. Question 131
State whether the statements are True or False.
A rhombus can be constructed uniquely, if both diagonals are given.

Q.

Using ruler and compasses only, draw an equilateral triangle of side 5 cm. Draw its inscribed circle. Measure the radius of the circle.

Q.

Draw an equilateral triangle of side 8 cm and its circumscribed circle. Find the length of the radius.

1. 4.61 cm

2. 2.61 cm

3. 8.4 cm

4. 6.0 cm

Q. A line intersects Y-axis and X-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the co-ordinates of P and Q.

Q. Question 173
Diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Give a figure to justify your answer.

Q.

Construct the quadrilateral ABCD in which AB = 5cm, BC = 7 cm and$\angle ABC={120}^0$, given that AC is its only line of symmetry. Name the quadrilateral.

1. Parallelogram

2. Rectangle

3. None of these

4. Kite

Q.

Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of lengths 5 cm and 4 cm respectively, using ruler and compasses only. Then the point of intersection of locus of points, inside the circle, that are equidistant from A and C and the locus of points, inside the circle, that are equidistant from A and B, is the centre of the circle.

1. True

2. False

Q.

Construct a $\Delta ABC$ in which AB = 4 cm, BC = 5 cm and $\angle ABC={120}^{\circ }$. Locate the point P, such that $\angle BAP={90}^{\circ }$ and BP = CP. Then the length of BP is

1. 5.1 cm

2. 5.6 cm

3. 6.1 cm

4. 6.6 cm

Q. Question 200
Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.

Q. Question 195
Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.

Q. Construct a $△ABC$ in which AB=6 cm, $\angle A={30}^{\circ }$ and $\angle B={60}^{\circ }$.Construct another $△A{B}^{\prime }{C}^{\prime }$ similar to $△ABC$ with base AB'=8 cm.

Q.

The given figure shows a triangle ABC in whcih AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.

Prove that:

(i) F is equidistant from A and B.

(ii) F is equidistant from AB and AC.

Q.

Draw a circle of radius 3 cm and mark two chords AB and AC of the circle of lengths 4 cm and 5 cm respectively, using ruler and compasses only. Then the locus of points, inside the circle, that are equidistant from A and C, passes through the centre of the circle.

1. True

2. False

Q.

The mean proportional of the line segments of length 4 cm and 7 cm is ________.(Use geometric method)

1. 2.5

2. 9.1

3. 5.3

4. 4.2

Q.

Draw a line $\overline{AB}=5cm$. Bisect $\overline{AB}$into two equal parts using compass

Q.

Plot the points A(2, 9), B(-1, 3) and C(6, 3) on a graph paer.On the same graph paper, draw the locus of point A so that the area of $△ABC$ remains the same as A moves.

Q.

State the locus of a point in a rhombus ABCD, which is equidistant

(i) from AB and AD;

(ii) from the vertices A and C.

Q.

Ali was asked to construct a square for which only the length of the diagonal alone is given. He was given a compass and a straight edge (a ruler with NO markings). The square is ACBD with AB as one of its diagonal. P is said to be the point of intersection of the diagonals of the square.
Which of the following is constructed as a first step in this construction?

1. AB or BD, P, AP or PB or OC or OD

2. AD or CD, P, AP or PB or OC or OD

3. AC or CD, P, AP or PB or OC or OD

4. B or CD, P, AP or PB or OC or OD

Q.

The mean proportional of the lines 6 cm & 4 cm is _________.

1. 4

2. 4.1

3. 4.9

4. 3

Q. Question 1
To divide a line segment AB in the ratio 5:7 first a ray AX is drawn so that $\angle$BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is
(A) 8
(B) 10
(C) 11
(D) 12​​​​​​​

Q.

The mean proportional of the line segment of lengths 4 cm and 2 cm is _____.

1. 3

2. 2.5

3. 4

4. 2

Q.

Construct rhombus ABCD with sides of length 5 cm and diagonal AC of length 7 cm. Find the point R on BC such that RA = RD. Then the length of CR is

1. 1.1 cm

2. 2.3 cm

3. 4.2 cm

4. 3.8 cm

Q.

Construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Find the point R on AD such that RB = RC. Then the length of AR is

1. 1.2 cm

2. 0.7 cm

3. 1.9 cm

4. 2.2. cm

Q.

The locus of centers of all circles passing through two given points A and B, is the perpendicular bisector the line segment AB.

1. True

2. False