CAT Practice : Coordinate Geometry

You are here: Home  CAT Questionbank   CAT Quant  Geometry: Triangles  Question 22
If you find the relation between the sides of sqaure , triangle and the radius , then you are through!!

Circle, Square and Triangle

    Q.22: A circle inscribed in a square of side 2 has an equilateral triangle inscribed inside it. What is the ratio of areas of the equilateral triangle to that of the square?
    1. 9 : 16
    2. 3 : 4
    3. 9 : 4
    4. 3 : 16


  • Correct Answer
    Choice (D). 3 : 16 units

Detailed Solution

The radius of the circle is 1 unit.
If we considered the side of the equilateral triangle to be ‘a’, the circumradius of an equilateral triangle is R = . a = .
So, ratio of areas of the equilateral triangle to that of the square is

2 : (2)2

3 : 4

3 : 16

Correct Answer: 3 : 16 units

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.