UPSC CDS 2 2020 Math Paper

In right angled triangle PCQ
PQ2=CQ2+PC2 ………..(1)
In Right angled triangle ABC
AB2=CB2+AC2 ………(2)
Adding (1) and (2)
⇒AB2+PQ2=CB2+AC2 +CQ2+PC2
⇒AB2+PQ2=(AC2+CQ2) +(CB2+PC2)
AB2+PQ2=AQ2+BP2
Hence, statement (1) is correct.
Consider statement (2)
Now,
AB = 2PQ is true only if P and Q are midpoints of AC and BC respectively.
But it is not mentioned in question that P and Q are midpoints of AC and BC respectively.
Hence, statement (2) is not correct.