Quantitative Aptitude – Geometry – ABC is a triangle with integer-valued

XAT 2021 Exam Paper – Quantitative Aptitude – Geometry – ABC is a triangle with integer-valued

Q. ABC is a triangle with integer-valued sides AB = 1, BC >1, and CA >1. If D is the midpoint of AB, then, which of the following options is the closest to the maximum possible value of the angle ACD (in degrees)?

1. 45
2. 60
3. 15
4. 30
5. 75

Answer: 15

Solutions:

Given, AB = 1, AC>1 and BC>1
If ABC was an equilateral triangle i.e if AB=AC=BC =1, ACD would have been 30.
As C moves away from A and B, the angle decreases, hence the angle should be less than 30 and among the given options only 15 is less than 30.

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