Category:Excenters and Incenter of Orthic Triangle
Jump to navigation
Jump to search
This category contains pages concerning Excenters and Incenter of Orthic Triangle:
Acute Triangle
Let $\triangle ABC$ be an acute triangle.
Let $\triangle DEF$ be the orthic triangle of $\triangle ABC$ such that:
- $D$ is on $BC$
- $E$ is on $AC$
- $F$ is on $AB$
Then:
- the excenter of $\triangle DEF$ with respect to $EF$ is $A$
- the excenter of $\triangle DEF$ with respect to $DF$ is $B$
- the excenter of $\triangle DEF$ with respect to $DE$ is $C$
and:
- the incenter of $\triangle DEF$ is the orthocenter of $\triangle ABC$.
Obtuse Triangle
Let $\triangle ABC$ be an obtuse triangle such that $A$ is the obtuse angle.
Let $\triangle DEF$ be the orthic triangle of $\triangle ABC$ such that:
Let $H$ be the orthocenter of $\triangle ABC$.
Then:
- the excenter of $\triangle DEF$ with respect to $EF$ is $H$
- the excenter of $\triangle DEF$ with respect to $DF$ is $B$
- the excenter of $\triangle DEF$ with respect to $DE$ is $C$
and:
- the incenter of $\triangle DEF$ is $A$.
Pages in category "Excenters and Incenter of Orthic Triangle"
The following 4 pages are in this category, out of 4 total.