UPSC 2016 CDS I Math Paper

In right ΔACQ,
AQ2=AC2+QC2 ....(1)
In right ΔBCP,
BP2=BC2+PC2 .....(2)
In right ΔPCQ,
PQ2=PC2+QC2 .....(3)
In right ΔACB,
AB2=BC2+AC2 ......(4)
Adding (1) and (2), we have
Adding (3) and (4), we have
From (5) and (6), we have
AQ2+BP2=PQ2+AB2