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RD Chapter 16 Circles Ex 16.2 Solutions

Question - 11 : - Given an arc of a circle, complete the circle.

Answer - 11 : -

Let PQ be an arc of the circle.
In order to complete the circle. First of all we have to find out its centre and radius.
Now take a point R on the arc PQ and join PR and QR.
Draw the perpendicular bisectors of PR and QR respectively.
Let these perpendicular bisectors intersect at point O.
Then OP = OQ, draw a circle with centre O and radius OP = OQ to get the required circle.

Question - 12 : - Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points?

Answer - 12 : -

Given that two different pairs of circles in the figure.
As we see that only two points A, B of first pair of circle and C, D of the second pair of circles are common points.
Thus only two points are common in each pair of circle.

Question - 13 : - Suppose you are given a circle. Give a construction to find its centre.

Answer - 13 : -

Given a circle C(O, r).
We take three points A, B and C on the circle.
Join AB and BC.
Draw the perpendicular bisector of chord AB and BC.
Let these bisectors intersect at point O.
Hence, O is the centre of circle.

Question - 14 : - Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are opposite side of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.

Answer - 14 : - Let AB and CD be two parallel chord of the circle with centre O such that AB = 5 cm, CD = 11 cm and PQ = 6 cm. Let the radius of the circle be  cm.

Draw and  as well as point O, Q, and P are collinear.
Clearly, PQ = 6 cm
Let OQ = x cm then
 
Join OA and OC, then
OA = OC = r
Now and  
So,   and  
In  we have
 
  …… (1)
And
 
  …… (2)
From (1) and (2) we get
 
 
 
 
 
Putting the value of x in (1) we get,
 

Question - 15 : - The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance of 4 cm from the centre, what is the distance of the other chord from the centre?

Answer - 15 : -

Let AB and CD be two parallel chord of the circle with centre O such that AB = 6 cm, CD = 8 cm and OP = 4 cm. let the radius of the circle be  cm.
According to the question, we have to find OQ
Draw   and  as well as point O, Q, and P are collinear.
Let  
Join OA and OC, then
OA = OC = r
Now  and  
So, AP = 3 cm and CQ = 4 cm
In  we have
And in  
 
 

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