The sides of a triangle are given by b 2 + c 2 , c 2 + a 2 , a 2 + b 2 . Where a , b , c > 0 , then the area of the triangle equals

1 2 b 2 c 2 + c 2 a 2 + a 2 b 2

3 2 a 2 b 2 + b 2 c 2 + c 2 a 2

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The line AB is $6 m$ in length and is the tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is

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Important Questions on Measurement

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IMPORTANT

Quantitative Aptitude for the CAT>Chapter 4 - Measurement>Practice Exercises>Q 6

Two chords of lengths a and b of a circle subtend

60 °

and

90 °

angles at the centre, respectively. Which of the following is correct?

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Quantitative Aptitude for the CAT>Chapter 4 - Measurement>Practice Exercises>Q 27

A circle is inscribed in an equilateral triangle and a square is inscribed in that circle. The ratio of the areas of the triangle and the square is

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Quantitative Aptitude for the CAT>Chapter 4 - Measurement>Practice Exercises>Q 29

In $∆ A B C, A B = A C = 28$ and $B C = 20 .$ Points $D, E$ and $F$ are on sides $\bar{A B}, \bar{B C}$ and $\bar{A C},$ respectively, such that $\bar{D E}$ and $\bar{E F}$ are parallel to $\bar{A C}$ and $\bar{A B},$ respectively. What is the perimeter of parallelogram. $A D E F ?$

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Quantitative Aptitude for the CAT>Chapter 4 - Measurement>Practice Exercises>Q 34

Let $C_{1}$ and $C_{2}$ be the inscribed and circumscribed circles of triangle with sides $3 cm$ , $4 cm$ and $5 cm$ . Then $\frac{area of C_{1}}{area of C_{2}}$ is :

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CAT

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Quantitative Aptitude for the CAT>Chapter 4 - Measurement>Practice Exercises>Q 35

The sides of a triangle are given by

\sqrt{b^{2} + c^{2}}, \sqrt{c^{2} + a^{2}}, \sqrt{a^{2} + b^{2}}

. Where

a, b, c > 0,

then the area of the triangle equals

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Quantitative Aptitude for the CAT>Chapter 4 - Measurement>Practice Exercises>Q 38

Δ A B C, A B = 86,

and

A C = 97 .

A circle with centre

A

and radius

A B

intersects

B C

at points

B

and

X .

Moreover

B X

and

C X

have integer lengths. What is

B C ?

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 4 - Measurement>Practice Exercises>Q 78

Consider two different cloth-cutting processes. In the first one,

n

circular cloth pieces are cut from a square cloth piece of side

a

in the following steps: the original square of side

a

is divided into

n

smaller squares, not necessarily of the same size, then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side

a

and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is

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CAT

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Quantitative Aptitude for the CAT>Chapter 4 - Measurement>Practice Exercises>Q 97

A certain city has a circular wall around it and this wall has four gates pointing North, South, East and West. A house stands outside the city, three kilometres North of the North gate and it can just be seen from a point nine kilometres East of the South gate. What is the diameter of the wall that surrounds the city?

The line AB is 6 m in length and is the tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is

Important Questions on Measurement

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The line AB is $6 m$ in length and is the tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is