A) 12
B) 15
C) 16
D) 18
Correct Answer: D
Solution :
\[\Delta RPQ\] is \[{{90}^{o}}\], \[{{45}^{o}}\] and \[{{45}^{o}}\] triangle i.e., isosceles triangle. \[\Rightarrow \] \[PQ=RQ=a\] and \[PR=a\sqrt{2}\] Also, as RDP and REQ are secants, then \[RD\times RP=RE\times RQ\] i.e., \[4\times a\sqrt{2}=(a-5\sqrt{2})\times a\] \[\Rightarrow \] \[4\sqrt{2}=a-5\sqrt{2}\Rightarrow a=9\sqrt{2}\] Thus, \[PR=(9\sqrt{2})\,\sqrt{2}=18\]
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