Locus of the Points Equidistant From a Given Point

Q. The locus of all the points equidistant from a single point is a circle.

1. True
2. False

Q.

Name the locus of points which are equidistant from two fixed points.

1. The angle bisector

2. A line

3. The circle

4. The perpendicular bisector

Q.

Does a circle have a focus?

Q.

Find the locus of midpoints of radii of a circle.

1. Concentric circle with half radius.

2. None of these

3. Circle with radius OA.

4. Circle with radius 2OA.

Q.

In the adjoining figure, DE || BC.
(i) If AD=3.4 cm, AB=8.5 cm and AC=13.5 cm, find AE.
(ii) If $\frac{AD}{DB}=\frac{3}{5}$ and AC=9.6 cm, find AE.

Q.

State and prove Thales Theorem.

Q.

The collection of all points in a plane which is equidistant from a fixed point is a

1. circle

2. triangle

3. rectangle

4. square

Q.

Describe the locus for questions 1 to 13 given below:

The locus of the door-handle, as the door opens.

Q. No of significant figure in 400m , 400 & 4.

Q.

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

(i) always 4 cm from the line AB.

(ii) 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.

Q.

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

(i) Equidistant from A and B.

(ii) Always 4 cm from the line AB.

(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.

1. Rectangle

2. Kite

3. Square

4. Parallelogram

Q. A circle touches two adjacent sides of a rectangle AB and AD at points P and Q respectively.Third vertex C of the rectangle lies on the circle. The length of perpendicular from vertex C to the chrod PQ is 5. Find the area of rectangle.

Q.

What is The locus of the door-handle, as the door opens?

Q.

Four different paths connect opposite corners of a square as shown above. Which of the following statement(s) holds true?

1. (iii) is the longest path

2. (i) is longer than (iv)

3. (ii) is longer than (ii)

4. all the paths are equal

Q.

The locus of the position of a person at the same distance from a tower is a _____.

1. straight line

2. square

3. circle

4. rectangle

Q. Locus of a point which is at a distance of 3 cm from the point O in the given diagram is:

1. 
2. 
3. 

Q.

Find the locus of the position of a person at the same distance from a tower.

1. Rectangle

2. Square

3. straight line

4. Circle

Q. In the given figure $DB\perp BC,DE\perp AB$ and $AC\perp BC$. Prove that $\frac{BE}{DE}=\frac{AC}{BC}$

Q. The sides AB and AC of ABC are produced to point P and Q respectively . If the bisectors of $\angle PBC$ and $\angle QCB$ meet at point O , then prove that $\angle BOC$ = 90 - $\frac{1}{2}$ $\angle A$ .

Q. A point has ___ dimension(s).

Q. Find the point which lies on the perpendicular bisector of the line segment joining the point A(-2, -5) and B(2, 5)

Q. Equation to the locus of a point equidistant from the points $A(1,3)$ and $B(-2,1)$ is

1. $4x+6y=5$
2. $-4x+6y=8$
3. None of these
4. $6x+4y=5$

Q. Locus of a point which is at a fixed distance from a given line are lines above and below the given line and parallel to it.

1. True
2. False

Q. What is the locus of the door-handle, as the door opens.

Q.

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

(i) Equidistant from A and B.

(ii) Always 4 cm from the line AB.

(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.

Q.

1. a point
2. a circle
3. a straight line
4. two straight lines

Q. The locus of centres of circles which touch two intersection lines is a

1. parabola
2. ellipse
3. straight line
4. circle

Q.

A straight line AB is 8 cm long. Locate by construction the locus of a point which is:

(i) Equidistant from A and B.

(ii) Always 4 cm from the line AB.

(iii) Mark two points X and Y, which are 4 cm from AB and equidistant from A and B, Name the figure AXBY.

Q. If you are in a trolley of a moving giant wheel, then your locus is a circle.

1. True
2. False

Q. Locus of a point which is equidistant from a fixed point is the circumference of a circle.

1. True
2. False