Question 4 (ii)

Question 4 (ii) following figure; P and Q the • on of tw o circles with centres O iotertstraight Vines APB and COD ue • to 00'; prove that • AB, CD

Dear Student,

Please find below the solution to the asked query:

As here we want to solve only second part of query ( 4 ) , So we assume that first part's solution you already have ( As that information needed in solution for second part ) , Then 

From first part we know :  OO' = $\frac{1}{2}$AB                                 --- ( 1 )

And our diagram , As :

Here we draw two perpendiculars from O to CQ and O' to DQ 

And we know if a perpendicular is drawn to any chord from center of circle then that perpendicular also bisect that chord , So

CM =  QM  = $\frac{1}{2}$ CQ                                        --- ( 2 )

And

DN =  QN  = $\frac{1}{2}$ DQ                                        --- ( 3 )

And

MN  =  QM  +  QN , Substitute values from equation 2 and 3 we get :

MN  = $\frac{1}{2}$ CQ +  $\frac{1}{2}$ DQ ,

MN  =  $\frac{1}{2}$ ( CQ + DQ ) ,

MN = $\frac{1}{2}$ CD

And here we also know :  Line CQD | | OO' and from construction we know OM $\perp$ CQ and O'N $\perp$ DQ , So we can say that

OMNO' is a rectangle and in rectangle opposite sides are equation in length , So  MN =  OO' that we substitute in above equation we get :


OO' = $\frac{1}{2}$ CD   , And from equation 1 we get 
$\frac{1}{2}$ AB = $\frac{1}{2}$ CD  ,

AB  =  CD                                                                   ( Hence proved )


Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards