Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 13

HARD

JEE Main

IMPORTANT

Earn 100

A circle having centre as $O'$ and radius $r'$ touches the incircle of $∆ A B C$ externally at $F,$ where $F$ is on $B C$ and also touches its circumcircle internally at $G .$ If $O$ is the circumcentre of $∆ A B C$ and $I$ is its incentre, then:

50% studentsanswered this correctly

Important Questions on Solutions and Properties of Triangle

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 1

If in a triangle

A B C, r_{1} + r_{2} + r_{3} = 9 r,

then the triangle is necessarily

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 2

In triangle

A B C, r = \frac{R}{6}

and

r_{1} = 7 r

. Then the measure of angle

A = ?

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 3

Find the value of

(r_{2} + r_{3}) \sqrt{\frac{r r_{1}}{r_{2} r_{3}}}

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 6 - Solutions and Properties of Triangle>DPP>Q 4

In a

∆ A B C

right angled at

A, \cos^{- 1} (\frac{R}{r_{2} + r_{3}})

is

HARD

JEE Main

IMPORTANT

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

If in a triangle $A B C, r_{1} = 2 r_{2} = 3 r_{3}$ and $D$ is the midpoint of $B C,$ then $\cos (∠ A D C)$ 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 6

In the ambiguous case if the remaining angle of a triangle with given

a, b, A

and

B_{1}, B_{2}, C_{1}, C_{2}

; then

\frac{\sin C_{1}}{\sin B_{1}} + \frac{\sin C_{2}}{\sin B_{2}} = ?

EASY

JEE Main

IMPORTANT

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

Two sides of a triangle are of lengths

\sqrt{6}

and

4

and the angle opposite to smaller side

30 °

, then how many such triangles are possible?

EASY

JEE Main

IMPORTANT

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

If circum radius of a triangle

A B C

is

2

, then the maximum value of

\frac{a b c}{a + b + c}

is?