Questions
The angle of a right angled triangle are The ratio of the in-radius and the perimeter is
a
(2−3):23
b
1:83(2+3)
c
(2+3):43
d
none of these
detailed solution
Correct option is A
Let ABC be the right angled triangle whose anglesare in A.P. Then,Now, A+B+C=180∘⇒3B=180∘⇒B=60∘So, let the angles be A=30∘,B=60∘ and C=90∘∴ asin30∘=bsin60∘=csin90∘=2R⇒ a=R,b=3R and c=2RAlso,Δ=12absin90∘=12ab=32R2∴ rs=Δs2⇒ rs=3R223R+2R)2−32×4(22=233+33+32⇒ rs=23(3−3)2(9−3)263(3−1)236=23(4−23)⇒ rs=2−33−⇒r2s=2−323Talk to our academic expert!
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