37. Exemplar exercise problems XII

1. Two tangents $PQ$ and $PR$ are drawn from an external point to a circle with centre $O$. Prove that $QORP$ is a cyclic quadrilateral.

 

2. If from an external point $B$ of a circle with centre $O$, two tangents $BC$ and $BD$ are drawn such that $\angle DBC = 120^\circ$, prove that $BC + BD = BO$, i.e., $BO = 2BC$.