Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of Triangler1,r–R formula basedMedium2 minQB

MathematicsMediumsingle choice

In triangle ABC, (s-r_2)/r_2= $2$ , where r_2 is the B-exradius. Find ( $a^{2}$ + $c^{2}$ - $b^{2}$ )/(2ac).

Options:

Answer:

Solution:

The requested expression is cos B by the cosine rule. Since r_2= $Δ$ /(s-b), (s-r_2)/r_2=s/r_2-1=(s-b)/r-1=cot(B/2)-1, since r_2= $Δ$ /(s-b), r= $Δ$ /s and tan(B/2)=r/(s-b).. Therefore cot(B/2)=1+ $2$ =cot22.5°, B=45° and cos B=1/ $2$ .

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:r1,r–R formula based

⏱ 2mℹ️ Source: QB

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