if a chord AB subtends an angle of 60 degree at the centre of a circle,then the angle between the tangents at A and B is also 60degree. true or false

In the quadrilateral AOBP 
$\angle$AOB = 60º (given)
$\angle OAP =\angle OBP =90°$(tangent is always perpendicular to the radius)
 $$\begin{gathered} \angle AOB+\angle OBP+\angle OAP+\angle APB = 360°(sum of the interior angles of a quadrilateral) \\ \Rightarrow 60°+90°+90°+\angle APB = 360° \\ \Rightarrow \angle APB = 360°-(60°+90°+90°) =360°-240° =120° \end{gathered}$$
hence we can conclude that angle between the tangents at A and B is not equal to the angle subtended by the chord AB
so the statement is false