7. CBQ - Tangents to the circle

A backyard is in the shape of a triangle \(ABC\) with right angle at \(B\). \(AB = 7 \ m\) and \(BC = 15 \ m\). A circular pit was dug inside it such that it touches the walls \(AC\), \(BC\) and \(AB\) at \(P\), \(Q\) and \(R\) respectively such that \(AP = x \ m\). 

 

 

Based on the above information, answer the following questions: 

 

(i) Find the length of \(AR\) in terms of \(x\).

 

(ii) Write the type of quadrilateral \(BQOR\). parallelogramsquarerectangletrapezium

 

(iii) (a) Find the length \(PC\) in terms of \(x\) and hence find the value of \(x\).

 

$\frac{i}{i}\left(\sqrt{i}-i\right)$ \(m\)

 

 

(b) Find \(x\) and hence find the radius \(r\) of circle.

 

$\frac{i}{i}\left(i-\sqrt{i}\right)$ \(m\)