Mathematics - Properties of Triangle Question with Solution | TestHub
MathematicsProperties of Triangler1,r–R formula basedMedium2 minQB
MathematicsMediumsingle choice
The exradii of triangle ABC are r_a,r_b,r_c. If r_a+r_b=3R and r_b+r_c=2R, find the smallest angle.
Options:
Answer:
B
Solution:
For any pair of exradii, e.g. r_a+r_b, the identity r_a+r_b=(2R)(1+cos C) follows from r_a=/(s-a), r_b=/(s-b) and Heron's formula. Thus 3R=2R(1+cos C), so cos C=1/2 and C=60°. Likewise 2R=2R(1+cos A), so cos A=0 and A=90°. B=30°, which equals (1/2)arctan.
Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:r1,r–R formula based
⏱ 2mℹ️ Source: QB
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