# Class 10 R S AGGARWAL AND V AGGARWAL Solutions Maths Chapter 9 - Constructions

## Constructions Exercise Ex. 9A

### Solution 1

### Solution 2(i)

Steps:

1. Draw AB = 8 cm

2. Draw ray AX making an acute angle of 45 degree with AB

3. Draw ray BY making an acute angle of 45 degree with AB

4. Mark four points A_{1}, A_{2},
A_{3}, A_{4} on AX and five points B_{1}, B_{2},
B_{3}, B_{4}, B_{5} on BY in such a way that AA_{1}=A_{1}A_{2}
=A_{2}A_{3}=A_{3}A_{4}=BB_{1}=B_{1}B_{2}=B_{2}B_{3}=B_{3}B_{4}=B_{4}B_{5}

5. Now join A4 B5

6. Let this intersect at C, which is the point that divided AB in 4:5 ratio

### Solution 2(ii)

### Solution 3

### Solution 4

** **

### Solution 5

Steps:

1. Construct ΔABC

2. Draw a ray BX making acute angle with BC

3. Mark
four points B_{1}, B_{2}, B_{3}, B_{4} on BY
in such a way that BB_{1}=B_{1}B_{2}=B_{2}B_{3}=B_{3}B_{4}

4. Join B_{4}
with C

5. Draw B_{3}C'
parallel to B_{4}C

6. Now draw C'A' parallel to AC

7. Hence, ΔA'BC' is the required triangle

### Solution 6

### Solution 7

### Solution 8

BC will be divided in the ratio 3 : 4

### Solution 9

### Solution 10

## Constructions Exercise Ex. 9B

### Solution 1

### Solution 2

### Solution 3

Steps:

1. Draw a circle of 3 cm

2. Draw AB diameter and extend AB on both sides such that OP = OQ = 7cm

3. Now draw perpendicular bisectors of OP and OQ, and let them bisect OP and OQ at S and T respectively

4. Now taking S as center and radius SP, cut arcs on the circle and join the points of intersection with P using straight line

5. Also, taking T as center and radius TQ, cut arcs on the circle and join the points of intersection with Q using straight line

6. Thus we have the required tangents

### Solution 4

### Solution 5

### Solution 6

### Solution 7

### Solution 8

### Solution 9

### Solution 10

### Solution 11

Steps

1. Draw two concentric circles of radii 3 cm and 5 cm with center O

2. Take a point A on circle and join AO

3. Now draw perpendicular bisector of AO, and let it bisect OA at B

4. Now, taking B as center and radius AB, cut arcs on the inner circle and join the points of intersection with A using straight line

5. Thus we have the required tangents

### Solution 12

Steps

1. Draw a circle of any radius with center O

2. Take a point A outside the circle and join AO

3. Now draw perpendicular bisector of AO, and let it bisect OA at B

4. Now, taking B as center and radius AB, cut arcs on the circle and join the points of intersection with A using straight line

5. Thus we have the required tangents

### Solution 13

Steps:

1. Draw a circle of radius 3 cm with center O

2. Take a point P outside the circle such that OP = 6.5 cm and join OP

3. Now draw perpendicular bisector of OP, and let it bisect OP at B

4. Now, taking B as center and radius PB, cut arcs on the circle and join the points of intersection with P using straight line

5. Thus we have the required tangents

## Constructions Exercise Test Yourself

### Solution 1

### Solution 2

### Solution 3

### Solution 4

### Solution 5

### Solution 6

### Solution 7

### Solution 8

### Solution 9

### Solution 10