Question

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Answer 1

The hypothesis should be that line ttis perpendicular to the radius OTOT at point TT on the circle of center OO. In that case, if PP is another point on tt, different from TT, then we have OP>OTOP>OT (hypotenuse is greater then leg). It follows that all points of tt, except TT, are external to the circle, and tt is thus a tangent.