In the given figure ABC is equilateral- If IB -6 cm- then IEA- 2-5 cmB- 3 cmC- 5 cmD- 4 cm

The correct option is B 3 cm ABC is equilateral .........(Given) In IBE , ∠ IBC = 30^∘ .........(Bi bisects ∠ ABC) sin30^∘ = r/R ...........(sin30^∘ = 1/2) ⇒ ...

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Standard X

Mathematics

Relation between Inradius and Perimeter of Triangle

In the given ...

Question

In the given figure $△ A B C$ is equilateral. If IB = 6 cm , then IE = ____.

2.5 cm

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3 cm

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5 cm

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4 cm

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Solution

The correct option is B
3 cm

$△ A B C$ is equilateral .........(Given)

In $△ I B E$ , $∠ I B C = 30^{\circ}$ .........(Bi bisects $∠ A B C$ )

sin $30^{\circ}$ = $\frac{r}{R}$ ...........(sin $30^{\circ}$ = $\frac{1}{2}$ )

$\Rightarrow$ r : R = IE : IB = 1 : 2

IB = 6 cm

$\Rightarrow$ IE = 3 cm

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In the given figure △ABC is equilateral. If IB = 6 cm , then IE = ____.

The correct option is B 3 cm △ABC is equilateral .........(Given) In △IBE , ∠IBC=30∘ .........(Bi bisects ∠ABC) sin30∘ = rR ...........(sin30∘ = 12) ⇒ r : R = IE : IB = 1 : 2 IB = 6 cm ⇒ IE = 3 cm

In the given figure $△ A B C$ is equilateral. If IB = 6 cm , then IE = ____.