Exam

Olympiad workbook

Subject

IOQM

Chapter

Straight Lines

Olympiad workbook · IOQM · Straight Lines

If A B C D is a rectangle and P is a point inside it such that A...

If $A B C D$ is a rectangle and $P$ is a point inside it such that $A P=33, B P=16, D P=63$. Find $C P$.

Step-by-step solution

$$\begin{aligned} & \text { In } \triangle P A D, x^2+y^2=33^2 ...(i) \\ & \text { In } \triangle P B D,(a-x)^2+y^2=16^2 ...(ii)\\ & \text { In } \triangle P D F, x^2+(b-y)^2=63^2 ....(iii)\\ & \begin{array}{r} \text { (ii) }+(\text { iii })-(\text { i }) \Rightarrow(a-x)^2+(b-y)^2 \\ \quad=63^2+16^2-33^2 \end{array} \\ & C P^2=56^2 \quad\left[\because \text { In } \triangle P C E, C P^2=(a-x)^2+(b-y)^2\right] \\ & C P=56 \end{aligned}$$