Three vertical poles of heights h1 - h2 and h3 at the vertices A- B and C of a - ABC subtend angles - - and - respectively at the cicumcentre of triangle- lf - - and - are in AP then h1- h2- h3 are in-

The correct option is C H. P we can see that , #160; tanα=h_1R⇒ h_1=Rtanα⇒ h_1=Rcotα Similarly, h_2=Rcotβ h_3=Rcotγ as we know that, ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sum of n Terms

Three vertica...

Question

Three vertical poles of heights $h_{1}$ , $h_{2}$ and $h_{3}$ at the vertices $A, B$ and $C$ of a $Δ A B C$ subtend angles $α, β$ and $γ$ respectively at the cicumcentre of triangle.
lf $cot α, cot β$ and $cot γ$ are in $A P$ then $h_{1}, h_{2}, h_{3}$ are in?

A . P

No worries! We‘ve got your back. Try BYJU‘S free classes today!

G . P

No worries! We‘ve got your back. Try BYJU‘S free classes today!

H . P

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

A . G . P

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $H . P$
we can see that ,
$t a n α = \frac{h_{1}}{R} \Rightarrow h_{1} = R t a n α \Rightarrow h_{1} = \frac{R}{c o t α}$

Similarly, $h_{2} = \frac{R}{c o t β} h_{3} = \frac{R}{c o t γ}$

as we know that, $c o t α, c o t β, cot γ$ are in $A P$

then, $h_{1}, h_{2}, h_{3}$ are in $H P$

Therefore, Answer is $C$

Suggest Corrections

Similar questions

Q. Three vertical poles of heights

h_{1}, h_{2}

and

h_{3}

at the vertices

A, B

and

C

of a

△ A B C

subtend angles

α, β, γ

respectively at the circumcentre of the triangle. If

cot α, cot β, cot γ

are in AP, then

h_{1}, h_{2}, h_{3}

are in

Q. The vertical poles of heights

h_{1}, h_{2}

and

h_{3}

at the vertices A,B and C of a

△ A B C

subtend angles

α, β

and

γ

respectively at the circumcentre of the triangle,If

cot α, cot β

and

cot γ

are in AP then

h_{1}, h_{2}, h_{3}

are in

Q. In

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

Let

A B C

be a triangle with altitudes

h_{1}, h_{2}, h_{3}

and inradius

r

Then

\frac{h_{1} + r}{h_{1} - r} + \frac{h_{2} + r}{h_{2} - r} + \frac{h_{3} + r}{h_{3} - r}

If a+b = $α$ ,ab = $β$ ,and a, $H_{1}$ , $H_{2}$ ,b form H.P,then $\frac{1}{H_{1}}$ + $\frac{1}{H_{2}}$ equals to

There are three setups, shown in figure. Voltage of ends are given, heat developed in 1, 2 and 3 are

H_{1}, H_{2}

and

H_{3}

, then

Join BYJU'S Learning Program

Three vertical poles of heights h1 , h2 and h3 at the verticesA, B and C of a ΔABC subtend angles α, β and γ respectively at the cicumcentre of triangle. lf cotα, cotβ and cotγ are in AP then h1, h2, h3 are in?

The correct option is C H. Pwe can see that , tanα=h1R⇒h1=Rtanα⇒h1=RcotαSimilarly, h2=Rcotβh3=Rcotγas we know that, cotα,cotβ,cotγ are in APthen, h1,h2,h3 are in HPTherefore, Answer is C

Three vertical poles of heights $h_{1}$ , $h_{2}$ and $h_{3}$ at the vertices $A, B$ and $C$ of a $Δ A B C$ subtend angles $α, β$ and $γ$ respectively at the cicumcentre of triangle.
lf $cot α, cot β$ and $cot γ$ are in $A P$ then $h_{1}, h_{2}, h_{3}$ are in?