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IMPORTANT

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If $A, A_{1}, A_{2}, A_{3}$ are the area of the incircle and excircles, then $\frac{1}{\sqrt{A_{1}}} + \frac{1}{\sqrt{A_{2}}} + \frac{1}{\sqrt{A_{3}}}$ is equal to

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Important Questions on Properties of Triangles, Heights and Distances

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 76

H

is the orthocentre of

Δ A B C

, then

A H

is equal to

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 77

A B C

is an isosceles triangle inscribed in a circle of radius

r

. If

A B = A C

and

h

is the altitude from

A

B C

then the triangle has perimeter

P = 2 (\sqrt{2 h r - h^{2}} + \sqrt{2 h r})

and area

A

(in sq. units) is equal to

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 78

In the given figure, $P$ is any interior point of the equilateral $∆ A B C$ of side length $2$ units.

Question Image

If $x_{a}, x_{b}$ and $x_{c}$ represent the distance of $P$ from the sides $B C, C A$ and $A B$ , respectively, then $x_{a} + x_{b} + x_{c}$ is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 10 - Properties of Triangles, Heights and Distances>Target Exercises>Q 79

Δ A B C,

base

B C

and area of triangle

' Δ'

are fixed. Locus of the centroid of

Δ A B C

is a straight line that 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 80

Δ A B C, ∠ A = \frac{π}{2}, A A_{1}

and

A A_{2}

are the median and altitude, respectively. If

∠ B A A_{1} = ∠ A_{1} A A_{2} = ∠ A_{2} A C,

then

\sin^{3} \frac{A}{3} \cdot \cos \frac{A}{3}

is equal to

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 81

At a point

A

, the angle of elevation of a tower is such that its tangent is

\frac{5}{12},

on walking

120 m

nearer the tower the tangent of the angle of elevation is

\frac{3}{4} .

The height of the tower 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 82

An observer on the top of a cliff

200 m

above the sea level, observes the angles of depression of two ships on opposite sides of the cliff to be

45 °

and

30 °

, respectively. The distance between the ships if the line joining them points to the base of cliff, 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 83

A tower is observed from two stations

A

and

B

, where

B

is East of

A

at a distance of

200 m

. The tower is due North of

A

and due West of

B .

The angles of elevation of the tower from

A

and

B

are complementary. The height of the tower is

If A,A1,A2,A3 are the area of the incircle and excircles, then 1A1+1A2+1A3 is equal to

Important Questions on Properties of Triangles, Heights and Distances

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If $A, A_{1}, A_{2}, A_{3}$ are the area of the incircle and excircles, then $\frac{1}{\sqrt{A_{1}}} + \frac{1}{\sqrt{A_{2}}} + \frac{1}{\sqrt{A_{3}}}$ is equal to