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Question -

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 -

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,
 

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