SSC CPO 2019 PYQ — Question 117

The correct answer is Option 3 i.e. a² = b² + bc

In ABC, AB = c cm, AC = b cm and CB = a cm and ∠A = 2∠B

Draw a line AD which is an angle bisector of angle A

⇒ ∠ABD = ∠BAD

⇒ AD = DB………………(1)

∠ADC = ∠DAB + ∠B = 2∠B = ∠CAB

∠CAD = ∠CAB − ∠DAB = ∠B

Here, △ACD∼△BCA (Using AA similarity criterion)

So, AC/BC = AD/AB

⇒ AC × AB = BC × AD………………..(2)

Also, AC/BC = CD/AC

⇒ AC² = BC × CD ………………..(3)

BC² = BC × (CD + DB) 

As, DB = AD

⇒ BC² = BC × (CD + DB) = BC × (CD + AD) = BC × CD + BC × AD 

⇒ BC² = AC² + AC × AB

⇒ a² = b² + bc