Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 42

HARD

JEE Advanced

IMPORTANT

Earn 100

In a $Δ A B C, R =$ circumradius and $r =$ inradius. Then $\frac{a \cos A + b \cos B + c \cos C}{a + b + c}$

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Important Questions on Properties of Triangles, Heights and Distances

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 43

In a

Δ A B C, 2 s =

perimeter and

R =

circumradius then

\frac{s}{R}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 44

In a

Δ A B C,

if

\frac{R}{r} \leq 2,

then the triangle is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 45

In the given figure, $P$ is any arbitrary interior point of the $Δ A B C, H_{a}, H_{b}$ and $H_{c}$ are the length of altitudes drawn from vertices $A, B$ and $C$ respectively. If $x_{a}, x_{b}$ and $x_{c}$ represent the distance of $P$ from sides $B C, A C$ and $A B$ , respectively, then $\frac{x_{a}}{H_{a}} + \frac{x_{b}}{H_{b}} + \frac{x_{c}}{H_{c}}$ is always equal to

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EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 46

In a

Δ A B C, a = 2 b

and

|A - B| = \frac{π}{3}

. The measure of

∠ C

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 47

If the sides of a right angled triangle are in

AP

, then tangents of the acute angled triangle are

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 49

If in an obtuse angled triangle the obtuse angle is

\frac{3 π}{4}

and the other two angles are equal to two values of

θ

satisfying

a \tan θ + b \sec θ = c,

where

|b| \leq \sqrt{a^{2} + c^{2}}

then

a^{2} - c^{2}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 50

The length of the sides of a triangle are

x, y

and

\sqrt{x^{2} + y^{2} + x y} .

The measure of the greatest angle is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 51

The greatest angle of a triangle whose sides are

x^{2} + x + 1, 2 x + 1

and

x^{2} - 1,

is