A backyard is in the shape of a triangle ABC with right angle at B . $A B=7 \mathrm{~m}$ and $B C=15 \mathrm{~m}$. A circular pit was dug inside it such that it touches the walls $\mathrm{AC}, \mathrm{BC}$ and AB at $\mathrm{P}, \mathrm{Q}$ and R respectively such that $A P=x \mathrm{~m}$. Based on the above information, answer the following questions: (i) Find the length of AR in terms of $x$. 1 (ii) Write the type of quadrilateral BQOR. 1 (iii)(a) Find the length PC in terms of $x$ and hence find the value of $x$. 2 OR

Explanation

The correct option is B because it asks to find x and hence find the radius r of the circle, which is the required solution.