Let us draw a circle in which AMB is an arc and M is the mid-point of the arc AMB. Joined AM and MB. Also TT' is a tangent at point M on the circle.
To Prove : AB || TT'
As M is the mid point of Arc AMB
Arc AM = Arc MB
AM = MB [As equal chords cuts equal arcs]
∠ABM = ∠BAM [Angles opposite to equal sides are equal] 
∠BMT' = ∠BAM [angle between tangent and the chord equals angle made by the chord in alternate segment] 
From  and 
∠ABM = ∠BMT'
So, AB || TT' [two lines are parallel if the interior alternate angles are equal]
Hence Proved !
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