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Similar Triangles

In Δ ABC ...

Question

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

\geq 4

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\geq 6

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\geq 2

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\geq 1

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Solution

The correct option is B $\geq 6$

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Similar questions

△ A B C

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

r

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

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

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

\frac{a}{R}

_{1}

_{2}

_{3}

\frac{1}{h_{1}} + \frac{1}{h_{2}} + \frac{1}{h_{3}} = ?

h_{1}, h_{2}

h_{3}

\frac{1}{h_{1}} + \frac{1}{h_{2}} + \frac{1}{h_{3}} = ?

Δ

A B C

A, B, C

a, b, c

a^{2} + b^{2} = c^{2}

R

r

R + r

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