Chapter 14 Practical Geometry Ex 14.1

Question 1.
Draw a circle of radius 3.2 cm.
Solution:
Step I : Mark a point O as a centre.
Step II: Open the compass up to the given radius 3.2 cm.

Step III : Put the needle of the compass at the centre O.
Step IV : Holding the top of the compass take one full round with pencil. The figure thus obtained is the required circle of radius 3.2 cm.

Question 2.
With the same centre O, Draw two circles of radius 4 cm and 2.5 cm.
Solution:
Step I : Take centre O and open the compass up to 4 cm. Step II : Draw a circle keeping the needle fixed at O.
Step III : Take the same centre O and open the compass up to 2.5 cm, and draw another circle.
The figure shows the required two circles with the same centre.

Question 3.
Draw a circle and any two its diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?
Solution:

(i) Draw a circle with centre 0 with suitable radius.
(ii) AB and CD are any two diameters.
(iii) On joining the end points of the diameters, we get a quadrilateral ACBD.
(iv) We note that OA = OB = OC = OD [Same radius]
and AC = DB, AD = BC
∠A = ∠C = ∠B = ∠D = 90°
Thus ACBD is a rectangle.
Again if the diameters are perpendicular to each other then on measuring, we get
AC = DB = AD = BC
Thus, ACBD is a square.

Question 4.
Draw any circle and mark points A, B and C such that
(a) A is on the circle
(b) B is in the interior of the circle
(c) C is in the exterior of the circle.
Solution:
Draw a circle with centre 0 and a suitable radius.
Here
(a) A is on the circle.
(b) B is in the interior of the circle.
(c) C is in the exterior of the circle.