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Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleLength of angle bisector and median / Dist. between sp. PointsMedium2 minQB

MathematicsMediumsingle choice

There is a point P inside triangle ABC such that $∠ P A B$ = $∠ PBC$ = $∠ PC A$ = $α$ . Let PA=x, PB=y, PC=z, $Δ$ be the area, and a,b,c be side lengths opposite A,B,C. Find tan $α$ .

Options:

Answer:

Solution:

This is the Brokard-angle relation cot $α$ = cot A + cot B + cot C. By the cosine rule, cot A=( $b^{2}$ + $c^{2}$ - $a^{2}$ )/(4 $Δ$ ); summing cyclically gives cot $α$ =( $a^{2}$ + $b^{2}$ + $c^{2}$ )/(4 $Δ$ ), hence option D.

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Length of angle bisector and median / Dist. between sp. Points

⏱ 2mℹ️ Source: QB

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