EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Properties of Triangle>JEE Advanced Paper 1 - 2021>Q 4

HARD

JEE Advanced

IMPORTANT

Earn 100

In a triangle $A B C$ , let $A B = \sqrt{23}, B C = 3$ and $C A = 4$ . Then the value of $\frac{\cot A + \cot C}{\cot B}$ is

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Important Questions on Properties of Triangle

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Properties of Triangle>JEE Advanced Paper 1 - 2020>Q 5

Let

x, y

and

z

be positive real numbers. Suppose

x, y

and

z

are the lengths of the sides of a triangle opposite to its angles

X, Y

and

Z

respectively. If

\tan \frac{X}{2} + \tan \frac{Z}{2} = \frac{2 y}{x + y + z}

, then which of the following statements is/are TRUE?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Properties of Triangle>JEE Advanced Paper 1 - 2019>Q 6

In a non-right-angled triangle

Δ P Q R,

let

p, q, r

denote the lengths of the sides opposite to the angles at

P, Q, R

respectively. The median from

R

meets the side

P Q

at

S,

the perpendicular from

P

meets the side

Q R

at

E

, and

R S

and

P E

intersect at

O .

If

p = \sqrt{3}, q = 1,

and the radius of the circumcircle of the

Δ P Q R

equals

1,

then which of the following options is/are correct?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Properties of Triangle>JEE Advanced Paper 1 - 2018>Q 7

In a triangle

P Q R,

let

∠ P Q R = 30 °

and the sides

P Q

and

Q R

have lengths

10 \sqrt{3} a n d 10

units, respectively. Then, which of the following statement(s) is (are) TRUE?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Properties of Triangle>JEE Advanced Paper 1 - 2016>Q 8

In a

△ X Y Z

let

x, y, z

be the lengths of sides opposite to the angles

X, Y, Z

respectively and

2 s = x + y + z .

If

\frac{s - x}{4} = \frac{s - y}{3} = \frac{s - z}{2}

and area of incircle of the triangle

△ X Y Z

is

\frac{8 π}{3}

, then