TheCATExam
Sign in

CAT 2004 — QA Question 34

2 CirclesEasy
Passage / Data

Answer the following question based on the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?

Answer & solution

  • A

    3-22

  • B

    4-22

  • C

    7-42

  • 6-42

Solution

AB = AK = 2

Quadrilateral ABCD is a square. 
∴ AC = 2√2

⇒ KC = AC - AK = 2√2 - 2

Let the centre of the smaller circle be O and let its radius be x. 

∴ OC = x√2 and KC = KO + OC = x + x√2

⇒ x + x√2 = 2√2 - 2

⇒ x = 22-21+2

⇒ x = (22-2)(1+2)×(2-1)(2-1) = 6 - 4√2

Hence, option (d).

CAT 2004 QA Q34: A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the — Solution | TheCATExam