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Trigonometry> how to find sides and angles of pedal tri...

question mark

how to find sides and angles of pedal triangle??

Rohit Falake , 10 Years ago

Grade 12th pass

1 Answers

Apoorva Arora

Last Activity: 10 Years ago

Given a point P inside the triangle ABC, The pedal triangle of P is the triangle whose polygon vertices are the feet of the perpendiculars from P to the sidelines. The pedal triangle of a triangle with trilinear coordinates $\alpha :\beta :\gamma$ and angles A B and C has trilinear vertex matrix
$\begin{bmatrix} 0 & \beta +\alpha cosC& \gamma +\alpha cosB\\ \alpha +\beta cosC& 0& \gamma +\beta cosA\\ \alpha +\gamma cosB & \beta +\gamma cosA& 0 \end{bmatrix}$

The side lengths are,

$a'=\frac{abc\sqrt{\beta ^{2}+\gamma ^{2}+2\beta \gamma cosA}}{2R|a\alpha +b\beta +c\gamma |}$

$b'=\frac{abc\sqrt{\alpha ^{2}+\gamma ^{2}+2\alpha \gamma cosB}}{2R|a\alpha +b\beta +c\gamma |}$

$c'=\frac{abc\sqrt{\alpha ^{2}+\beta ^{2}+2\alpha\beta \gamma cosC}}{2R|a\alpha +b\beta +c\gamma |}$

where R is the circumradius of the triangle ABC.
Thanks and Regards
Apoorva Arora
IIT Roorkee
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