CAT 2019 Question Paper | Quants Slot 1

CAT Questions

Geometry & specifically circles are tested multiple times in all CAT previous year paper. CAT 2019 question paper is no different with its share of these tough questions. Our recommendation would be for you to include Geometry in your CAT Preparation plan as these questions can be cracked with adequate preparation. Spend enough time grasping the concepts and then move on to practicing with CAT Previous Year Paper.

Question 21 : AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to

1. 8.5
2. 9.3
3. 9.1
4. 7.8

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Video Explanation

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Explanatory Answer

We know that angle APB = AQB = 90^o
We know PB = 6, AB = 10 and AP = 2AQ
From using Pythagorean triplet, we find that AP = 8 cms
So, AQ = 4cms
AQ² + QB² = AB²
16 + QB² = 100
QB² = 84
QB = 9.3

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The question is "AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to "

Hence, the answer is 9.1

Choice C is the correct answer.