Trigonometry

Q. The incircle of a scalene triangle $ABC$ touches side $AB,BC$ and $AC$ at $P,Q$ and $R$ respectively. If $O$ is the incentre of triangle $ABC,$ then which of the following statements is (are) correct?

$\text{I.}$ Area of $△OBC$ is $\frac{1}{2}\times BC\times \text{radius of incircle}$
$\text{II.}$ $AB+CQ=BQ+AC$
$\text{III.}$ Area of $△ABC$ is $\frac{1}{2}\times \text{perimeter of}△ABC\times \text{radius of incircle}$

1. $\text{I}$ and $\text{III}$
2. $\text{I}$ only
3. $\text{II}$ and $\text{III}$
4. $\text{I},\text{II}$ and $\text{III}$