22. Exemplar example problems III

Write 'True' or 'False' and give reasons for your answer.

 

1. In given figure, \(BOA\) is a diameter of a circle and the tangent at a point \(P\) meets \(BA\) extended at \(T\). If \(\angle PBO = 30^\circ\), then \(\angle PTA\) is equal to \(30^\circ\).

 

 

2. In given figure, \(PQL\) and \(PRM\) are tangents to the circle with centre \(O\) at the points \(Q\) and \(R\), respectively and \(S\) is a point on the circle such that \(\angle SQL = 50^\circ\) and \(\angle SRM = 60^\circ\). Then \(\angle QSR\) is equal to \(40^\circ\).