Question

As shown in the figure. two concentric circles are given and line AB is the tangent to the smaller circle at T. Shown that T is the midpoint of Seg AB 

Answer 1

proof OT is  perpendicular to AB (as AB = tangent)

other Method -

In ΔAOT, ΔOTB

∠OTB = ∠OTB = 90°

OT = OT = common 

OA = OB = radii

∴ ΔAOT ≅ ΔBOT

∴ At = BT ( by cpct) 

Now, we know that if a perpendicular is drawn to any chord from the centre, it bisects the chord.

∴ AT = TB 

Hence, This midpoint of AB.