In △ABC, ∠C = 90º. Points P and Q are on the sides AC…

In △ABC, ∠C = 90º. Points P and Q are on the sides AC and BC, respectively, such that AP : PC = BQ : QC = 1 : 2.

Then , (AQ² + BP²)/(AB)²/2 is equal to:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. $\frac {26}{9}$ .

Concept

Pythagoras theorem

Application

⇒ AP : PC = BQ : QC = 1 : 2

In ΔCAQ

⇒ CA² + CQ² = AQ²

⇒ AQ² = (3x)² + (2x)²

⇒ AQ² = 13x²

⇒ BP² = 13x²(Similarly)

In ΔABC

⇒ AC² + BC² = AB²

⇒ AB² = (3x)² + (3x)² = 18x²

Putting the respective values of (AQ² + BP²)/(AB)²/2

⇒ (13x² + 13x²)/18x²/2

⇒ 26x²/9x²

⇒ 26/9

SSC CGL 2020 PYQ — Question 76