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

HARD

JEE Advanced

IMPORTANT

Earn 100

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?

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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 - 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