UPSC CDS 2 2020 Math Paper

In a quadrilateral ABCD, ∠B = 90°AB2+BC2+CD2−AD2=0 …………….(1)
In right angled triangle ABC
⇒AC2=AB2+BC2 ……………(2)
Put the value of (2) in (1)
⇒AC2+CD2−AD2=0
⇒AC2+CD2=AD2 ……………..(3)
From (3), we can conclude that triangle ACD is a right angled triangle.
⇒ ∠ACD = 90°