QJEEM21Ma9ddd: JEE Main 2021 Mathematics - Class 11 JEEM21Ma9ddd Solution: In Δ ABC, the lengths of sides AC and AB are 12 cm and 5 cm,…

Question

Verified Solution • 2025–26 Session moderate

In

Δ

ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of

Δ

ABC is 30 cm² and R and r are respectively the radii of circumcircle and incircle of

Δ

ABC, then the value of 2R + r (in cm) is equal to ___________.

Accepted Answer

Area =

\frac{1}{2} (5) (12) \sin θ = 30

\sin θ = 1 \Rightarrow θ = \frac{π}{2}

Δ

is right angle

Δ

r = (s - a) \tan \frac{A}{2}

r = (s - a)

\tan \frac{90}{2}

r = (s - a)

2 R + r = s

, (As

a = 2 R

)

2 R + r = \frac{5 + 12 + 13}{2} = 15

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