SSC CPO 2019 PYQ — Question 116

In ABC, AB = c cm, AC = b cm and CB = a cm. If ∠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

that △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)

Consider, (BC)² = BC × (CD + DB)

From (1) , DB = AD

(BC)² = BC × (CD + DB) = (BC)² = BC × (CD + AD)(BC × CD) +(BC × AD)

= (BC)² = (AC)² + (AC × AB)

= a² = b² + bc