Skills in Mathematics Trigonometry for JEE Main & Advanced>Chapter 3 - Properties and Solutions of Triangles>Objective Questions>Q 26

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Two sides of a triangle are given by the roots of the equation $x^{2} - 2 \sqrt{3} x + 2 = 0 .$ The angle between the sides is $\frac{π}{3}$ The perimeter of the triangle 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 27

If in a $Δ A B C$ , $\sin^{3} A + \sin^{3} B + \sin^{3} C = 3 \sin A \cdot \sin B \cdot \sin C,$ then the value of the determinant $|\begin{array}{l} a & b & c \\ b & c & a \\ c & a & b \end{array}|$ is

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

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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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