XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

XAT Previous Year Paper | XAT QADI Questions | Question 5

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Question 5 : Ramesh and Reena are playing with triangle ABC. Ramesh draws a line that bisects ∠BAC; this line cuts BC at D. Reena then extends AD to a point P. In response, Ramesh joins B and P. Reena then announces that BD bisects ∠PBA, what a surprise! Together, Ramesh and Reena find that BD= 6 cm, AC= 9 cm, DC= 5 cm, BP= 8 cm, and DP = 5 cm.

How long is AP?

  1. 11.5 cm
  2. 11.75 cm
  3. 10.5 cm
  4. 11 cm
  5. 10.75 cm

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Explanatory Answer

Mid point theorem
It is given that AD bisects the ∠BAC
By angle bisector theorem, \(\frac{A B}{A C}\) = \(\frac{B D}{D C}\) 
Hence AB = \(\frac{6}{5} \times 9\) = 10.8
Now Reena annouoces that BD bisects ∠ABP
Again by angle bisector theorem, \(\frac{B P}{A B}\) = \(\frac{P D}{A D}\)
AD = \(\frac{10.8}{8} \times 5=6.75\) 
Therefore, the length of AP = AD + DP = 6.75 + 5 = 11.75cm

The answer is '11.75 cm'

Choice B is the correct answer.

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