27. Exemplar exercise problems II

1. In given figure, \(AB\) is a chord of the circle and \(AOC\) is its diameter such that \(\angle ACB = 50^\circ\). If \(AT\) is the tangent to the circle at the point \(A\), then \(\angle BAT\) is equal to

 

2. From a point \(P\) which is at a distance of \(13 \ cm\) from the centre \(O\) of a circle of radius \(5 \ cm\), the pair of tangents \(PQ\) and \(PR\) to the circle are drawn. Then the area of the quadrilateral \(PQOR\) is