Is line AB tangent to the circle

no it is not a tangent
for it to be a tangent to the circle Angle A would have to be a right angle.
to check if its a right angled triangle, you can use pythagoras.
[tex] \sqrt{ {7.5}^{2} + {16}^{2} } = 17.67059...[/tex]
this shows it is not a right angled triangle because this calculation does not give us 10.3
therefore it is not a tangent and there is no right angle