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XAT 2022 — QA & DI Question 3

Geometric CentersEasy

Ramesh and Reena are playing with triangle ∠ABC. Ramesh draws a line that bisects ; 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, hat 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?

Answer & solution

  • A

    11.5 cm

  • 11.75 cm

  • C

    10.5 cm

  • D

    11 cm

  • E

    10.75 cm

Solution

​​​​​​​

Given:
BD = 6 cm, AC = 9 cm, DC = 5 cm, BP = 8 cm, and DP = 5 cm.
Since AD is the angular bisector applying the angular bisector theorem we have:

ABBD = ACCD

Hence : Considering AB = x cm.

95 = x6

x = 10.8 cm.
Now since BD is the angular bisector for angle PBA we have :
Applyinh the internal angle bisector theorem:

PBPD = BAAD

Considering AD = y cm.

85 = 10.8y

y = 6.75 cm.
AP = AD + DP.
= 6.75 + 5 = 11.75 cm

XAT 2022 QA & DI Q3: Ramesh and Reena are playing with triangle ∠ABC. Ramesh draws a line that bisects ; this line cuts BC at D — Solution | TheCATExam