Mathematics - Properties of Triangle Question with Solution | TestHub
MathematicsProperties of TriangleLength of angle bisector and median / Dist. between sp. PointsMedium2 minQB
MathematicsMediumsingle choice
In triangle ABC, A=2/3, AB=x, and AB·AC=1. As x varies, find the largest possible length of internal angle bisector AD.
Options:
Answer:
C
Solution:
AB=x, AC=1/x and cos(A/2)=1/2. Bisector length AD=[2(AB)(AC)/(AB+AC)]cos(A/2)=1/(x+1/x)≤1/2, equality at x=1.
Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Length of angle bisector and median / Dist. between sp. Points
⏱ 2mℹ️ Source: QB
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