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Standard VI

Mathematics

Lines in a Triangle

In Δ ABC ...

Question

In $Δ$ $A B C$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.
The distance between circumcenter $O$ and incenter $I$ is?

\sqrt{R^{2} - 2 R}

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\sqrt{R^{2} - 2 r}

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\sqrt{R^{2} - 2 r R}

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\sqrt{R - 2 r R}

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Solution

The correct option is C $\sqrt{R^{2} - 2 r R}$

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Similar questions

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively. Let

r

and

R

be the inradius and the circumradius of the triangle, then the distance between the circumcenter and the incenter of

Δ A B C

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively. Let

r_{1}

and

r_{2}

be the ex-radius of the traingle.

In a triangle

A B C, \frac{r_{1} + r_{2}}{1 + cos C}

is equal to?

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively, then

r_{1}^{2} + r_{2}^{2} + r_{3}^{3} + r^{2} = ?

(where

r

=

in-radius, R

=

circumradius,

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

are ex-radii)

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively. Let

r_{1} . r_{2}

and

r_{3}

be the ex-radii of the traingle and

r

be the in-radius.

Find the value of

r_{1} + r_{2} + r_{3} - r

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

Then the

\frac{a^{2} + b^{2} + c^{2}}{R^{2}}

has the maximum value of?

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In Δ ABC the sides opposite to angles A,B,C are denoted by a,b,c respectively.The distance between circumcenter O and incenter I is?

The correct option is C √R2−2rR

In $Δ$ $A B C$ the sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively.
The distance between circumcenter $O$ and incenter $I$ is?

The correct option is C $\sqrt{R^{2} - 2 r R}$