Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 28

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Let $A_{0}, A_{1}, A_{2}, A_{3}, A_{4}$ and the $A_{5}$ be the consecutive vertices of a regular hexagon inscribed in a unit circle. The product of the lengths of $A_{0} A_{1}, A_{0} A_{2}$ and $A_{0} A_{4}$ is

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Important Questions on Properties and Solutions of Triangles

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 29

If

A

is the area and

2 s

the sum of three sides of a triangle, then

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 30

If

a, b, c, d

are the sides of a quadrilateral, then the minimum value of

\frac{a^{2} + b^{2} + c^{2}}{d^{2}}

is

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 31

In a

Δ P Q R, P S

is the angle bisector of

∠ P .

Then for

P S

which of the following is true

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 32

In a

Δ P Q R,

if

\cos^{2} \frac{P}{2} + \cos^{2} \frac{Q}{2} + \cos^{2} \frac{R}{2} = y (x^{2} + \frac{1}{x^{2}}),

then maximum value of

y

is :

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 33

In an isosceles right

Δ A B C,

the value of

\frac{I P}{O P}

is, (where

P

is orthocentre,

I

is incentre,

O

is circumcentre)

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 34

Consider a triangle

A B C .

C C_{1}

and

B B_{1}

are the medians drawn through angular points

B

and

C

, respectively and

{}^{'}G^{'}

is the centroid of

Δ A B C .

If the points

A, C_{1}, G

and

B_{1}

are concyclic, then

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 35

If

a, b, c

are sides of the

Δ A B C,

such that

{(1 + \frac{b - c}{a})}^{a} \cdot {(1 + \frac{c - a}{b})}^{b} \cdot {(1 + \frac{a - b}{c})}^{c} \geq 1

, then triangle

A B C

must be

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Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 36

In a

Δ

with sides

a, b

and

c

, a semicircle touching the sides

A C

and

C B

is inscribed whose diameter lies on

A B .

Then the radius of the semicircle is