Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 22

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A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length $3, 4$ and $5$ units. Then area of the triangle is equal to:

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Important Questions on Properties of Triangle

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Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 23

In a

Δ A B C, a = 1

and the perimeter is six times the arithmetic mean of the sines of the angles. Then measure of

∠ A

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 24

Three equal circles of radius unity touches one another. Radius of the circle touching all the three circles is-

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Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 25

Triangle

A B C

is isosceles with

A B = A C

and

B C = 65 cm

.

P

is a point on

B C

such that the perpendicular distances from

P

to

A B

and

A C

are

24 cm

and

36 cm

, respectively. The area of the triangle

A B C

(in sq. cm) is

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Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 26

In a

Δ A B C,

the value of

\frac{a \cos A + b \cos B + c \cos C}{a + b + c}

is equal to-

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Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 27

In a triangle

A B C,

if

a : b : c = 3 : 7 : 8,

then

R : r

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 28

If

r_{1} = 2 r_{2} = 3 r_{3},

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 29

In a

△ A B C,

following relations hold good. In which case(s) the triangle is a right angled triangle?

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Alpha Question Bank for Engineering: Mathematics>Chapter 33 - Properties of Triangle>Exercise-2>Q 30

The perimeter of a triangle

A B C

right angled at

C

is

70,

and the inradius is

6,

then

| a - b |

equals