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JEE Main 2021
Properties of Triangle
Properties of Triangle
Easy

Question

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

Answer: 1

Solution

Area = 12(5)(12)sinθ=30{1 \over 2}(5)(12)\sin \theta = 30 sinθ=1θ=π2\sin \theta = 1 \Rightarrow \theta = {\pi \over 2} Δ\Delta is right angle Δ\Delta r=(sa)tanA2r = (s - a)\tan {A \over 2} r = (s - a)$$$$\tan {{90} \over 2} r=(sa)r = (s - a) 2R+r=s2R + r = s, (As a=2Ra = 2R) 2R+r=5+12+132=152R + r = {{5 + 12 + 13} \over 2} = 15

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