8.1.15

       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°

  

                In Δ ABC 

                ∠ C = 60°

                ∠ B = 60

               ∠A  = 60 ( ∵ remaining angle )

∴ Δ ABC is equilateral.