An extension of Carnot’s theorem

We consider the following problem and the special cases of it as the applications. Let I be an arbitrary point in plane of triangle ABC such that I(\alpha,\beta,\gamma) in barycentric coordinates, let d_a,d_b,d_c be signed distance from I to side BC,CA,AB of triangle ABC. Then xd_a+yd_b+zd_c=\frac{x\alpha bc+y\beta ca+z\gamma ab}{2R(\alpha+\beta+\gamma)} with circumradii R.



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s

%d bloggers like this: