SSC GD Constable 2011 · Question 21 of 97

A point D is taken from the side BC of a right angled triangle ABC, where AB is hypotenuse. Then,

AAB2 + CD2 = BC 2 + AD2Correct
BCD2 + BD2 = 2AD2
CAB2 + AC 2 = 2AD2
DAB2 + AD2 = BD2

Answer: A. AB2 + CD2 = BC 2 + AD2

Explanation

△ ABC is a right angled triangle right angled at C ⇒ AB2 = AC 2 + BC 2 ( From Pythagoras theorem ) ⇒ AC 2 = AB2 − BC 2 From △ACD, AD2 = AC 2 + CD2 Substituting AC 2 = AB2 − BC 2 in above equation AD2 = AB2 − BC 2 + CD2 2 2 2 2 (11) ⇒ AB2 + CD2 = BC 2 + AD2

Source: Solved SSC GD 2011 Paper with Solutions — Testbook · reliable-secondary

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