Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 11

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The radii $r_{1}, r_{2}, r_{3}$ of the escribed circles of triangle $A B C$ are in harmonic progression. Let area of triangle $A B C$ be $24$ and its perimeter be $24 .$ Then which of the following is/(are) correct?

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Important Questions on Solutions and Properties of Triangle

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 1

In a triangle

A B C,

∠ A = 55 °, ∠ B = 15 °, ∠ C = 110 ° .

Then

c^{2} - a^{2}

is equal to

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 2

In triangle

A B C

, if

2 a = \sqrt{3} b + c

, then possible relation is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 3

A circle of area $20 sq units$ is centered at the point $O .$ Suppose $∆ A B C$ is inscribed in that circle and has area $8 sq units$ . The central angles $α, β$ and $γ$ are as shown in the figure. The value of $(\sin α + \sin β + \sin γ)$ is equal to

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 4

In

Δ A B C, b c = 2 b^{2} \cos A + 2 c^{2} \cos A - 4 b c \cos^{2} A,

then

∆ A B C

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 5

Given a triangle

∆ A B C

, such that

\sin^{2} A + \sin^{2} C = 1001 \times \sin^{2} B .

Then the value of

\frac{2 (\tan A + \tan C) \cdot \tan^{2} B}{\tan A + \tan B + \tan C}

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 6

∆ A B C

has different side lengths

a, b, c .

If

a^{2}, b^{2}, c^{2}

as sides form another

Δ P Q R,

then

Δ A B C

will always be

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 7

In

∆ A B C, ∠ B = \frac{π}{4}, ∠ C = \frac{π}{6} .

D

is a point on

B C

which divides it in the ratio

1 : 3, ∠ D A B = β

, then

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Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 8

The acute angle of a rhombus whose side is the geometric mean of its diagonals, is