In - ABC- the lengths of sides AC and AB are 12 cm and 5 cm- respectively- If the area of - ABC is 30 cm2 and R and r are respectively the radii of circumcircle and incircle of - ABC- then the value of 2R - r in cm is equal to

Area nbsp;=12(5)(12)sinθ =30 ⇒sinθ =1⇒θ =π2 ABC is right angled at A. r=(s a) tanA2 ⇒ r = s a ⇒2R + r = s nbsp; nbsp; ( ∵ a=2R ) ⇒ 2R+r=302=15 ...

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Standard X

Mathematics

Heights and Distances

In Δ ABC, the...

Question

In $Δ A B C,$ the lengths of sides $A C$ and $A B$ are $12 cm$ and $5 cm,$ respectively. If the area of $Δ A B C$ is $30 {cm}^{2}$ and $R$ and $r$ are respectively the radii of circumcircle and incircle of $Δ A B C,$ then the value of $2 R + r$ $(in cm)$ is equal to

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Solution

Area $= \frac{1}{2} (5) (12) sin θ = 30$
$\Rightarrow sin θ = 1 \Rightarrow θ = \frac{π}{2}$
$A B C$ is right angled at $A .$

$r = (s - a) tan \frac{A}{2}$
$\Rightarrow r = s - a$
$\Rightarrow 2 R + r = s (∵ a = 2 R)$
$\Rightarrow 2 R + r = \frac{30}{2} = 15$

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In ΔABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of ΔABC is 30 cm2 and R and r are respectively the radii of circumcircle and incircle of ΔABC, then the value of 2R+r (in cm) is equal to

Area =12(5)(12)sinθ=30 ⇒sinθ=1⇒θ=π2 ABC is right angled at A. r=(s−a)tanA2 ⇒r=s−a ⇒2R+r=s (∵a=2R) ⇒2R+r=302=15

In $Δ A B C,$ the lengths of sides $A C$ and $A B$ are $12 cm$ and $5 cm,$ respectively. If the area of $Δ A B C$ is $30 {cm}^{2}$ and $R$ and $r$ are respectively the radii of circumcircle and incircle of $Δ A B C,$ then the value of $2 R + r$ $(in cm)$ is equal to

Area $= \frac{1}{2} (5) (12) sin θ = 30$
$\Rightarrow sin θ = 1 \Rightarrow θ = \frac{π}{2}$
$A B C$ is right angled at $A .$

$r = (s - a) tan \frac{A}{2}$
$\Rightarrow r = s - a$
$\Rightarrow 2 R + r = s (∵ a = 2 R)$
$\Rightarrow 2 R + r = \frac{30}{2} = 15$