8.1.14

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14. Through the point of intersection of two circles two straight lines AB and CD are drawn meeting one circle at A , C and the other at B and D. Prove AC // BD. 
Given:    : Two circles intersect at X and Y.
AB and CD are drawn meeting one circle at A , C and the other at B and D.

To Prove :  :AB // CD

Proof :   : We draw XY. 

                 ACYX and BDYX are inscribed in a circles respectively. 
                α = ∠ D
                β = ∠ C

              α + β = 180 

          ∴ ∠ D + ∠C = 180

          ∴ AB // CD

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