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

The correct option is D HP #160; R / h _ 1 =α #160; , etc where R is circumradius #160;As α , β , γ #160; is A.P #160;⇒ 1 / h _ 1 , 1 / ...

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Standard XII

Mathematics

Sum of n Terms

The vertical ...

Question

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

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Solution

The correct option is D HP
$\frac{R}{h_{1}} = cot α$ , etc where R is circumradius
As $cot α, cot β, cot γ$ is A.P
$\Rightarrow \frac{1}{h_{1}}, \frac{1}{h_{2}}, \frac{1}{h_{3}}$ are in A.P

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The vertical poles of heights h1,h2 and h3 at the vertices A,B and C of a △ABC subtend anglesα,βand γ respectively at the circumcentre of the triangle,If cotα,cotβ and cotγ are in AP then h1,h2,h3 are in

The correct option is D HPRh1=cotα , etc where R is circumradius As cotα,cotβ,cotγ is A.P⇒1h1,1h2,1h3 are in A.P

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

The correct option is D HP
$\frac{R}{h_{1}} = cot α$ , etc where R is circumradius
As $cot α, cot β, cot γ$ is A.P
$\Rightarrow \frac{1}{h_{1}}, \frac{1}{h_{2}}, \frac{1}{h_{3}}$ are in A.P