HARD

JEE Main

IMPORTANT

Earn 100

In a triangle $A B C, D$ is a point on $B C$ such that $A D$ is the internal bisector of $∠ A .$ Let $∠ B = 2 ∠ C$ and $C D = A B .$ Then $∠ A$ is:

100% studentsanswered this correctly

Important Questions on Solutions and Properties of Triangle

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 5

∆ A B C

, the circumradius is

3

units and the inradius is

1.5

units. The value of a

a \cot^{2} A + b^{2} \cot^{3} B + c^{3} \cot^{4} C

is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 6

A D, B E, C F

are internal angular bisectors of

∆ A B C

and

I

is the incentre. If

a (b + c) \sec \frac{A}{2} I D + b (a + c) \sec \frac{B}{2} I E + c (a + b) \sec \frac{C}{2} I F = k a b c,

then the value of

k

is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 7

∆ A B C

, it is given that the distance between the circumcentre

(O)

and orthocentre

(H)

R \sqrt{1 - 8 \cos A \cos B \cos C} .

Q

is the mid-point of

O H

, then

A Q

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 8

In any

∆ A B C,

the line joining the circumcentre

(O)

and incentre

(I)

is parallel to

A C,

then

O I

is equal to

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 9

Let the incircle of a

∆ A B C

touch the sides

B C, C A

and

A B

D, E

and

F

, respectively. Let the area of

∆ A B C

△

and that of

D E F

∆^{'} .

a, b

and

c

are sides of

∆ A B C,

then the value of

a b c (a + b + c) \frac{∆^{'}}{∆^{3}}

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 10

Let

H

be the orthocentre of triangle

A B C .

Then the angle subtended by side

B C

at the centre of incircle of

∆ C H B

is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 11

Let

P

be an interior point of

∆ A B C .

∠ A = 45 °, ∠ B = 60 °

and

∠ C = 75 °

. If

X =

area of

∆ P B C,

Y =

area of

∆ P A C

and

Z =

area of

∆ P A B,

then which of the following is/are true?

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 12

Let

l

be the length of median from the vertex

A

to the side

B C

of a

∆ A B C .

Then:

In a triangle ABC, D is a point on BC such that AD is the internal bisector of ∠A. Let ∠B=2∠C and CD=AB. Then ∠A is:

Important Questions on Solutions and Properties of Triangle

Learn and Prepare for any exam you want !

In a triangle $A B C, D$ is a point on $B C$ such that $A D$ is the internal bisector of $∠ A .$ Let $∠ B = 2 ∠ C$ and $C D = A B .$ Then $∠ A$ is: