Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 13

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In $∆ A B C, ∠ C = 2 ∠ A$ and $A C = 2 B C$ . Then which the following is/are true

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Important Questions on Properties of Triangle

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 14

If in a triangle

A B C, θ

is the angle determined by

\cos θ = \frac{(a - b)}{c}

, then:

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Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 15

If in a triangle

A B C, \cos A \cos B + \sin A \sin B \sin C = 1,

then the triangle is

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Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 16

If in a

Δ A B C, a = 5, b = 4

and

\cos (A - B) = \frac{31}{32}

, then

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Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 17

In a triangle

A B C,

points

D

and

E

are taken on side

B C

such that

B D = D E = E C .

If angle

A D E =

angle

A E D = θ,

then-

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Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 18

In a triangle

A B C, \frac{a}{b} = 2 + \sqrt{3}, ∠ C = 60 °

, then in the triangle

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Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 19

In a

Δ A B C, a \cos B + b \cos C + c \cos A = \frac{a + b + c}{2}

then

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Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 20

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?

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 5 - Properties of Triangle>Exercise 1>Q 21

Let

a, b, c

be the sides of a triangle

A B C

such that

a = 2 c, \cos (A - C) + \cos B = 1

. Then the value of

C

is