Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

how to find sides and angles of pedal triangle??

Apoorva Arora IIT Roorkee
6 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,
$a'=\frac{abc\sqrt{\beta ^{2}+\gamma ^{2}+2\beta \gamma cosA}}{2R|a\alpha +b\beta +c\gamma |}$
$b'=\frac{abc\sqrt{\alpha ^{2}+\gamma ^{2}+2\alpha \gamma cosB}}{2R|a\alpha +b\beta +c\gamma |}$
$c'=\frac{abc\sqrt{\alpha ^{2}+\beta ^{2}+2\alpha \beta cosC}}{2R|a\alpha +b\beta +c\gamma |}$
where R is the circumradius of the triangle ABC.
Thanks and Regards
Apoorva Arora
IIT Roorkee