Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 10

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

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If the hypotenuse of a right-angled triangle is four times the length of the perpendicular drawn from the opposite vertex to it, then the difference of the two acute angles will be

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Important Questions on Solution of Triangle

MEDIUM

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 11

In a

△ A B C

, if

\frac{r}{r_{1}} = \frac{r_{2}}{r_{3}},

then

EASY

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 12

In triangle

A B C,

internal angle bisector

∠ A

makes an angle

θ

with side

B C

. The value of

\sin θ

is

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KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 13

In an acute angled triangle

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

and

∠ B > \frac{π}{3}

, then

EASY

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 14

If

I

is the in-centre of a

∆ A B C

, then the ratio

I A : I B : I C

is equal to

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 15

In

∆ A B C

, the bisector of the angle

A

meets the side

B C

at

D

and the circumscribed circle at

E

, then

D E

equals

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 16

Two medians drawn from the acute angles of a right-angled triangle intersect at an angle

\frac{π}{6}

. If the length of the hypotenuse of the triangle is

3

units, then the area of the triangle (in sq. units) is

HARD

KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 17

In

∆ A B C,

the median

A D

divides

∠ B A C

such that

∠ B A D : ∠ C A D = 2 : 1

. Then

\cos (\frac{A}{3})

is equal to

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KVPY Aptitude Test - Stream SA

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 3 - Solution of Triangle>Exercise>Q 18

In triangle

A B C, \sum \sin \frac{A}{2} = \frac{6}{5}

and

\sum I I_{1} = 9

(where

I_{1}, I_{2}

and

I_{3}

are excentres and

I

is incentre), then circumradius

R

is equal to