Coincide

Infinite.

AB = 6 cm.

The measurements of angle that are marked on protractor are 0° to 180°.

First of all, we construct a line \(\bar{PQ}\) of length 7 cm.
Step I Place the zero mark of the ruler at P.
Step II Mark a point Q at a distance 7 ern from P.
                    
Step III Mark another point A between P and Q at distance 3.2 cm from P such that PA = 3.2 cm.
Step IV Measure line segment \(\bar{QA}\). We fin4 that \(\bar{QA}\) = 7.0 - 3.2 = 3.8 cm.

Given, radius of circle is 3 cm.
Steps of construction are as follows:
Step I Draw a circle of radius 3 cm.
Step II Draw two perpendicular diameters AB and CD.
                  
Step III Join A and D, D and B, Band C and A and C.
Thus, quadrilateral ABCD is a square.

Construct a perpendicular to a line from a point on it.
                   
Here, \(\angle\)PAR = 90^o.

Let the fourth number be x.
Case I. Taking the correct number 12

∴ LCM=3 \(\times\) 5 \(\times\) 7 \(\times\) x
Case II. Taking 21 instead of 12

∴ LCM = 3 \(\times\) 5 \(\times\) 7 \(\times\) x
According to the question,
LCM is the same in both the cases.
∴  Fourth number = 4 x 7 = 28.

Ratio of income to expenditure = 7 : 5
Let the income and expenditure per month be Rs 7x and 5x respectively.
Then, saving per month = Rs 7x - Rs 5x = Rs 2x
According to the question,
2x= 2000
⇒ x =\(\frac{2000}{2}\) =1000
⇒ 7x = 7 x 1000 = 7000
Hence, his income is Rs 7000 per month.

Given, \(\bar{AB}\) = 7.8 cm and \(\bar{AC}\) = 4.7 cm. Now, to construct a line segment of length 7.8 cm, we use the following steps:
Step I Draw a line, I. Mark, a point A on this line.
Step II Place the pointer of compasses at the zero mark of the ruler. Open it to place the pencil point up to the 7.8 ern mark.
Step III Without changing the opening to the compasses. Place the pointer on A and swing an arc to cut 1 at B.
Step IV \(\bar{AB}\) is a line segment of length 7.8 cm.
                     
Now, to cut-off \(\bar{AC}\) of length 4.7 cm from \(\bar{AB}\), we use the following steps:
Step V Now, place the pointer of compasses at the zero mark of the ruler. Open it to the place the pencil point up to 4.7 cm mark.
Step VI Without changing the opening of the compasses, place the pointer on A and swing an arc to cut 1 at C.
                     
Step VII Now \(\bar{AC}\)is a line segment of length 4.7 cm. On measuring, we get \(\bar{BC}\) =3.1 cm.
                    

To make a copy of \(\bar{PQ}\), we use the following steps
Step I Firstly, draw \(\bar{PQ}\) of any length, because length is not known.
                      
Step II Fix the compasses pointer on P and the pencil end Q. The opening of the instrument now gives the length of \(\bar{PQ}\).
                        
Step III Draw any line I and choose a point C on it. Without changing the compasses setting, place the pointer on C.
                        
Step IV Swing an arc that cuts I at a point, say D. Then, \(\bar{CD}\) is copy of \(\bar{PQ}\).
                           

 To construct the perpendicular bisector of chord \(\bar{AB}\), we use the following steps:
Step I Draw a circle with C as centre and radius 3.4 em.
Step II Now, draw a chord AB of the circle (a chord of a circle is a line segment joining any two points on the circle).
Step III With A as centre, using compasses draw an arc (here, we can draw circle also) with radius more than half of the length of \(\bar{AB}\).
Step IV With the same radius and with B as centre, draw an another arc using compasses. Let it cut the previous arc at P and C.
Step V Join \(\bar{PC}\) and produced up to Q. It cuts \(\bar{AB}\) at O.
Therefore, \(\bar{PC}\) is the perpendicular bisector of \(\bar{AB}\).
                         
Also, the perpendicular bisector \(\bar{PC}\) passes through the centre C of the circle.
Hence, the perpendicular bisector of chord AB passes through the centre C.