Steps of Construction:

1. Draw a circle with radius 7 cm having centre O

2. Take any point Q on the circumference of the circle and join OQ

Now, given angle between the two tangents is half of the central angle made by joining the point of contacts to the centre of the circle.

We know that radius is perpendicular to the tangent at the point of tangency,

So, angle between two tangent + central angle = 360 - 90 - 90 = 180 degrees

=>  angle between two tangent + 2( angle between two tangent) = 180

=> 3( angle between two tangent) = 180

=>  angle between two tangent =180/3

=>  angle between two tangent = 60

=> Central angle = 60 degrees

3. Now take any radius (less than half of OQ) and centre O, draw an arc that intersects our line at A and with same radius and centre A

draw another arc that intersects our previous arc at B and again with the same radius and centre B, draw another arc that intersects 

the main arc at C

4. Join OC and extend that line intersect our circumference at R

5. Now with the same radius and centre Q, draw another arc that intersects the line OQ at D with same radius and centre D, draw

another arc that intersects the previous arc at E and again with the same radius and centre E, draw another arc that intersects the main arc

main arc at F. Now with the same radius and take centre E and F, we draw arcs that intersect at G. 

6.  Again with the same radius and centre R, draw another arc that intersects the line OR at H with same radius and centre H, draw

another arc that intersects the previous arc at I and again with same radius and centre I, draw another arc that intersects the main arc

at J. Now with the same radius and take centre I and J, we draw arcs that intersect at K. 

7. Line QG and RK extend and meet at P.

Now, from the figure,

∠QOR = 120 degree and ∠QPR = 60 degree