Mathematics - Properties of Triangle Question with Solution | TestHub
MathematicsProperties of Triangler1,r–R formula basedMedium2 minQB
MathematicsMediumsingle choice
In triangle ABC, the incenter and circumcenter are reflections of one another in side BC. Find (degrees).
Options:
Answer:
B
Solution:
Reflection in BC fixes B and C, so BI=BO=R and CI=CO=R; hence BI=CI and B=C. Further BI=r/sin(B/2)=R, so r/R=sin(B/2). Euler's identity r/R=4 sin(A/2)sin(B/2)sin(C/2), and B=C, yields 4 sin(A/2)sin(B/2)=1. With B=(180°-A)/2, solve A=108°.
Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:r1,r–R formula based
⏱ 2mℹ️ Source: QB
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