If \(AP\) and \(AQ\) are the two tangents to a circle with center \(O\), such that \(\angle POQ = 110^\circ\), then \(\angle PAQ =\):
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The angle between two tangents drawn from an external point to a circle is supplementary to half of the angle between the lines joining the external point to the center of the circle.
For a circle with tangents from an external point, the angles between the tangents and the line joining the external point to the center of the circle are equal.
Given that \(\angle POQ = 110^\circ\), and \(\angle PAQ\) is the angle between the two tangents, we use the fact that the sum of the angles \(\angle PAQ\) and \(\angle POQ\) must be 180° (because they are supplementary).
Thus, we have:
\[
\angle PAQ = 180^\circ - \frac{\angle POQ}{2} = 180^\circ - \frac{110^\circ}{2} = 180^\circ - 55^\circ = 70^\circ
\]
Thus, the correct answer is option (2).
