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Question

Two chords AB, CD of length 5 cm, 11 cm respectively of a circle are parallel. If the distance between AB and CD is 3 cm. find the radius of the circle.Assume that the chords are on the same side of the center.


  1. 5.02cm

  2. 7.02cm

  3. 8.02cm

  4. 6.02cm


Solution

The correct option is D

6.02cm


Given: Chord AB=5 cm, chord CD = 11 cm and AB  CD.

Perpendicular distance ML between AB and CD = 3 cm.

To find: Radius of the circle.

Construction:Join OB, OD and draw perpendicular bisectors OL of AB and OM of CD.

 ln right angled triangle OMD, OD2 = MD2OM2         [By PythagorasTheorem]

Let OM = x cm

r2(112)2x2    ..........(i)
And In right triangle OLB, OB2 = BL2OL2   [By Pythagorastheorem]

r2(52)23+x2   .........(ii)

From (i) and (ii), we get

r2  =  (112)2 +x2(52)23+x2

1214x2254 + 9 + x2 + 6x

 x2 -  x2 + 6x = 1214254 - 9

6x = 12125364604 - 15

x = 156 cm - 52 cm

From (1),  r2 =  (112)2(52)2 -  121+2541464

r =  (146)2 cm
 

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