EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 32 - Properties of Triangle>JEE Main - 9th April 2017>Q 6

HARD

JEE Main

IMPORTANT

Earn 100

The lengths of two adjacent sides of a cyclic quadrilateral are $2$ units and $5$ units and the angle between them is $60^{o}$ . If the area of the quadrilateral is $4 \sqrt{3}$ sq. units, then the perimeter of the quadrilateral is

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Important Questions on Properties of Triangle

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 32 - Properties of Triangle>JEE Main - 25 June 2022 Shift 1>Q 7

Let

a, b

and

c

be the length of sides of a triangle

A B C

such that

\frac{a + b}{7} = \frac{b + c}{8} = \frac{c + a}{9}

. If

r

and

R

are the radius of incircle and radius of circumcircle of the triangle

A B C

, respectively, then the value of

\frac{R}{r}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 32 - Properties of Triangle>JEE Main - 28 July 2022 Shift 1>Q 8

Let

C

be the centre of the circle

x^{2} + y^{2} - x + 2 y = \frac{11}{4}

and

P

be a point on the circle. A line passes through the point

C

, makes an angle of

\frac{π}{4}

with the line

C P

and intersects the circle at the points

Q

and

R

. Then the area of the triangle

P Q R

(in

{unit}^{2}

) is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 32 - Properties of Triangle>JEE Main - 1 February 2023 Shift 1>Q 9

For a triangle

A B C

, the value of

\cos 2 A + \cos 2 B + \cos 2 C

is least. If its inradius is

3

and incentre is

M

, then which of the following is NOT correct?