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Hess' Law

In a ABC, the...

Question

In a $△$ ABC, the inradius is r and three exradii are $r_{1}, r_{2} a n d r_{3}$ respectably. In usual notations the value of $r . r_{1} . r_{2} . r_{3}$ is equal to

A

2∆

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B

∆²

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C

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D

None of these

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Solution

The correct option is B
∆²

$r . r_{1} . r_{2} . r_{3} = \frac{△}{s} . \frac{△}{s - a} . \frac{△}{s - b} . \frac{△}{s - c} = \frac{△^{4}}{△^{2}} = △^{2}$

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Similar questions

Δ A B C,

the inradius and three exradii are

r, r_{1,} r_{2}

r_{3}

respectively, in usual notations. The value of

r . r_{1} . r_{2} . r_{3}

Δ A B C,

the inradius and three exradii are

r, r_{1^{'}} r_{2}

r_{3}

In usual notations the value of

r . r_{1} . r_{2} . r_{3}

Q. Assertion :In a

△ A B C

a < b < c

r

is inradius and

r_{1}, r_{2}, r_{3}

are the axradii opposite to angle

A, B, C

respectively, then

r < r_{1} < r_{2} < r_{3}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1}

is equal to
(where

r_{1}, r_{2}

r_{3}

are the exradii and

2 s

is the perimeter.)

Q. In a triangle

A B C, r^{2} + r_{1}^{2} + r_{2}^{2} + r_{3}^{2} + a^{2} + b^{2} + c^{2}

is equal to (where

r

is inradius and

r_{1}, r_{2} . r_{3}

a, b, c

are the sides of

△ A B C

)

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