**Answer
1** :

Steps of construction :

(i) Draw a line segment AB = 8.6 cm.

(ii) With centres A and B, and radius more than half of AB, draw arcs which intersect each other at E and F, on both sides of AB.

(iii) Join EF which intersects AB at D.

D is the required mid point of AB.

Measuring each part, it is 4.3 cm long.

**Answer
2** :

Steps of construction :

(i) Draw a line segment AB = 5.8 cm.

(ii) With centres A and B and radius more than half of AB, draw arcs intersecting each other at E and F.

(iii) Join EF which is the required perpendicular bisector of AB.

**Answer
3** :

Steps of construction :

(i) Draw a circle with centre O and radius 5 cm.

(ii) Draw a chord AB of the circle.

(iii) With centres A and B and radius more than half of AB draw arcs intersecting each other at P and Q.

(iv) Join PQ which intersects AB at D and passes through O, the centre of the circle.

**Answer
4** :

Steps of construction :

(i) Draw a circle with centre O and a suitable radius.

(ii) Draw two chords AB and CD which are not parallel to each other.

(iii) Draw the perpendicular bisectors of AB and CD with the help of ruler and compasses. We see that these two chords intersect each other at the centre O, of the circle.

**Answer
5** :

Steps of construction :

(i) Draw a line segment AB = 10 cm.

(ii) With the help of ruler and compasses, bisect AB at C.

(iii) Bisect again AC at D.

Measuring AD, it is 2.5 cm long.

**Answer
6** :

Steps of construction :

(i) Draw a line segment AB.

(ii) With the help of ruler and compasses, draw the bisector of AB which bisects AB at C.

(iii) Similarly, in the same way draw the bisector of AC at D.

We see that AC = 1/2 (AB).

**Answer
7** :
Steps of construction :

(i) Draw a line segment AB.

(ii) Draw a ray AX makingan acute angle with A3 and equal 4 parts at A_{1}, A_{2}, A_{3} andA_{4}.

(iii) JoinA_{4}B.

(iv) From A3, draw a lineparallel to A_{4}B which meets AB at C.

C is the required point and AC = 3/4 (AB).

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