Relation between circumradius- side lengths and area of the triangle can be given by R - abc -4 - where a - b - c represent the sides and - represents the areaA- TrueB- False

The correct option is A TrueWe already know, Δ = 1/2ab sin c from sine rule ......(1) and R=c/2 sin C .........(2) Substituting (2) in (1) Δ = 1/2ab ( C/2R )⇒ ...

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Standard XII

Mathematics

Pedal Triangle

Relation betw...

Question

Relation between circumradius, side lengths and area of the triangle can be given by $R = \frac{a b c}{4 Δ}$ where a, b, c represent the sides and $Δ$ represents the area

True

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False

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Solution

The correct option is A True
We already know, $Δ = \frac{1}{2} a b s i n c$ from sine rule ......(1)
and $R = \frac{c}{2 s i n C}$ .........(2)
Substituting (2) in (1)
$Δ = \frac{1}{2} a b (\frac{C}{2 R}) \Rightarrow R = \frac{a b c}{4 Δ}$
$∴$ The given statement is true.

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Similar questions

Q. Prove that: acosA + bcosB + ccosC=∆/R
where a,b,c are the sides of a triangle and A,B,C are it's angles and ∆ is the area of the triangle ABC and R is the circumradius.

Δ

A B C

the sides opposite to angles

A, B, C

are denoted by

a, b, c

respectively.

a^{2} + b^{2} + c^{2} = 8 R^{2},

where

R =

circumradius, then the triangle is?

Q. In

△ A B C, 8 Δ = (b + c) (b c + 1)

, then circumradius of

△ A B C

is (

Δ

denotes area of triangle and

a, b, c

are length of sides

B C, A C

and

A B

respectively)

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

Q. In a triangle

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R (b + c) = a \sqrt{b c},

where

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Then the triangle is

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Relation between circumradius, side lengths and area of the triangle can be given by R=abc4Δ where a, b, c represent the sides and Δ represents the area

The correct option is A TrueWe already know, Δ=12absinc from sine rule ......(1) and R=c2sinC .........(2) Substituting (2) in (1) Δ=12ab(C2R)⇒R=abc4Δ ∴ The given statement is true.

Relation between circumradius, side lengths and area of the triangle can be given by $R = \frac{a b c}{4 Δ}$ where a, b, c represent the sides and $Δ$ represents the area

The correct option is A True
We already know, $Δ = \frac{1}{2} a b s i n c$ from sine rule ......(1)
and $R = \frac{c}{2 s i n C}$ .........(2)
Substituting (2) in (1)
$Δ = \frac{1}{2} a b (\frac{C}{2 R}) \Rightarrow R = \frac{a b c}{4 Δ}$
$∴$ The given statement is true.