Myint Mo Htun Thit

       Draw a circle and a tangent TAS meeting it at A. Draw a chord AB making m ∠ TAS = 60• and another chord BC // TS. Prove that Δ ABC is equilateral.  Given :   :  a tangent TAS meeting at A                   m ∠ TAS = 60°                   BC // TS To Prove :     : Δ ABC is equilateral Proof :    : In θO                   ∠ C = ∠ TAS ( ∵ Theorem 4)                    ∠ C = 60°                    ∠C = ∠ SAC ( ∵ BC // TS )                   ∴  ∠ SAC = 60                     ∠ SAC = ∠ B ( ∵ Theorem 4 )                   ∴ ∠B = 60° ...

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