State whether the following statement is True or False and provide a reason for your answer:
$A$ pair of tangents can be constructed to a circle inclined at an angle of $170^{\circ}$.
$A$ pair of tangents can be constructed to a circle inclined at an angle of $170^{\circ}$.
(A) True.
In a circle,the angle between the two tangents drawn from an external point and the angle subtended by the line segments joining the points of contact to the center are supplementary (i.e.,they add up to $180^{\circ}$).
Let the angle between the tangents be $\theta$ and the angle at the center be $\phi$.
We know that $\theta + \phi = 180^{\circ}$.
Since the angle between the tangents is given as $170^{\circ}$,the angle at the center would be $180^{\circ} - 170^{\circ} = 10^{\circ}$.
Since $10^{\circ} > 0^{\circ}$,it is geometrically possible to construct such a pair of tangents.
In a circle,the angle between the two tangents drawn from an external point and the angle subtended by the line segments joining the points of contact to the center are supplementary (i.e.,they add up to $180^{\circ}$).
Let the angle between the tangents be $\theta$ and the angle at the center be $\phi$.
We know that $\theta + \phi = 180^{\circ}$.
Since the angle between the tangents is given as $170^{\circ}$,the angle at the center would be $180^{\circ} - 170^{\circ} = 10^{\circ}$.
Since $10^{\circ} > 0^{\circ}$,it is geometrically possible to construct such a pair of tangents.
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