XAT 2022 Geometry & Mensuration Question (Hard)

Question

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. Together, Ramesh and Reena find that BD 6 cm, AC 9 cm, DC 5 cm, BP 8 cm, and D

Optima Learn · Accepted Answer

First, AD bisects BAC and meets BC at D. By the angle bisector theorem in triangle ABC, BD DC AB AC. Given BD 6, DC 5, and AC 9, we have AB 9 6 5, so AB 6 5 9 54 5 10.8 cm. Next, AD is extended to P, so A, D, P are collinear. In triangle PBA, BD bisects PBA and meets PA at D, so by the angle bisecto

XAT 2022 Geometry & Mensuration — Previous Year Question

XAT 2022

Quantitative

Geometry & Mensuration

Hard

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