In the given figure , two concentric circles are given and line AB is tangent to the smaller circle at T. Show that T is the mid point of seg AB.

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Solution

In $△$ AOT and $△$ BOT, we have:

$∠$ ATO = $∠$ BTO = 90 $°$ (Tangent is perpendicular to the radius)
AO = BO (Radius of the larger circle)
OT = OT (Common)
By RHS congruency, $△$ AOT $≅$ $△$ BOT
i.e., AT = BT (CPCT)
∴ T is the midpoint of AB.

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