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 $BC = BD$.