Mathematics - Properties of Triangle Question with Solution | TestHub
MathematicsProperties of Triangler1,r–R formula basedMedium2 minQB
MathematicsMediumsingle choice
Let I be the incenter of triangle ABC, where BC⃗/|BC| + BA⃗/|BA| = BI⃗/k. Find its circumcircle diameter.
Options:
Answer:
C
Solution:
The sum of unit vectors from B along BC and BA points along BI and has length 2cos(B/2). Hence BI=2k cos(B/2). Since BI=r/sin(B/2) and r=4R sin(A/2)sin(B/2)sin(C/2), 2R=k cos(B/2)/[sin(A/2)sin(C/2)] = k sin[(A+C)/2]/[sin(A/2)sin(C/2)] = k[cot(A/2)+cot(C/2)].
Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:r1,r–R formula based
⏱ 2mℹ️ Source: QB
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