35. Exemplar exercise problems X

Write 'True' or 'False' and justify your answer in each of the following:

 

1. If a number of circles pass through the end points \(P\) and \(Q\) of a line segment \(PQ\), then their centres lie on the perpendicular bisector of \(PQ\).

 

2. \(AB\) is a diameter of a circle and \(AC\) is its chord such that \(\angle BAC = 30^\circ\). If the tangent at \(C\) intersects \(AB\) extended at \(D\), then \(BC = BD\).