SSC CGL 2017 PYQ — Question 81

The correct answer is Option 2 i.e.8.

ΔABC is an isosceles right–angled triangle having ∠C = 90°

In the right angle ∆ABC

AC² + CB² = AB²

And

AC = BC (Given)

So,

2BC² = (AD + DB)²

⇒ 2BC² = AD² + DB² + 2AD × BD ---- (1)

In right-angled ∆CED:

CD² = CE² + ED² ------ (2)

In right-angled ∆CEB:

BC² = CE² + BE² ------ (3)

From equation 2 and 3:

BC² – CD² = BE² – DE²

⇒ BC² – CD² = (BE + DE) (BE – DE)

⇒ BC² – CD² = (AE + DE) (BE – DE)

⇒ BC² – CD² = AD × BD ------ (4)

From equations 1 and 4:

2BC² = AD² + DB² + 2BC² – 2CD²

⇒ AD² + DB² = 2CD²

CD² = 4

⇒ AD² + DB² = 2 × 4

⇒ AD² + DB² = 8