geometry
posted by Aaa
Let the incircle of triangle $ABC$ be tangent to sides $\overline{BC}$, $\overline{AC}$, and $\overline{AB}$ at $D$, $E$, and $F$, respectively. Prove that triangle $DEF$ is acute.
I have tried proving that triangle DEF's angles were les than the opposite angles in triangle ABC, but that wasn't really complete. Can anyone help?

PsyDAG
What do all the dollar signs ($) signify?

Atticus Finch
They're just a format you can ignore them

AoPS
Please do not post the questions we give you for homework to other websites.
Respond to this Question
Similar Questions

geometry
Points D, E, and F are the midpoints of sides \overline{BC}, \overline{CA}, and \overline{AB} of \triangle ABC, respectively, and \overline{CZ} is an altitude of the triangle. If \angle BAC = 71^\circ, \angle ABC = 39^\circ, and \angle … 
geometry
Points D, E, and F are the midpoints of sides \overline{BC}, \overline{CA}, and \overline{AB} of \triangle ABC, respectively, and \overline{CZ} is an altitude of the triangle. If \angle BAC = 71^\circ, \angle ABC = 39^\circ, and \angle … 
Geometry
Points D, E, and F are the midpoints of sides \overline{BC}, \overline{CA}, and \overline{AB} of \triangle ABC, respectively, and \overline{CZ} is an altitude of the triangle. If \angle BAC = 71^\circ, \angle ABC = 39^\circ, and \angle … 
math
Points $D$, $E$, and $F$ are the midpoints of sides $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$, respectively, of $\triangle ABC$. Points $X$, $Y$, and $Z$ are the midpoints of $\overline{EF}$, $\overline{FD}$, and $\overline{DE}$, … 
math
Points $D$, $E$, and $F$ are the midpoints of sides $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$, respectively, of $\triangle ABC$. Points $X$, $Y$, and $Z$ are the midpoints of $\overline{EF}$, $\overline{FD}$, and $\overline{DE}$, … 
Geometry
Triangle $ABC$ is isosceles with point $A$ at the point $(2, 7)$, with point $B$ at $(2, 0)$ and with point $C$ at $(3, 1).$ Triangle $ABC$ is reflected over $\overline{BC}$ to form $\triangle A'BC$. Triangle $A'BC$ is reflected … 
geometry
Points $F$, $E$, and $D$ are on the sides $\overline{AB}$, $\overline{AC}$, and $\overline{BC}$, respectively, of right $\triangle ABC$ such that $AFDE$ is a square. If $AB = 12$ and $AC = 8$, then what is $AF$? 
Geometry
In $\triangle ABC$, we have $AB = AC = 13$ and $BC = 10$. Let $M$ be the midpoint of $\overline{AB}$ and $N$ be on $\overline{BC}$ such that $\overline{AN}$ is an altitude of $\triangle ABC$. If $\overline{AN}$ and $\overline{CM}$ … 
math
Triangle $ABC$ is a right triangle with right angle at $A$. Suppose $\overline{AX}$ is an altitude of the triangle, $\overline{AY}$ is an angle bisector of the triangle, and $\overline{AZ}$ is a median of the triangle, and $\angle … 
geometry
Isosceles $\triangle{ABC}$ has a right angle at $C$. Point $P$ is inside $\triangle{ABC}$, such that $PA=11$, $PB=7$, and $PC=6$. Legs $\overline{AC}$ and $\overline{BC}$ have length $s=\sqrt{a+b\sqrt{2}}$, where $a$ and $b$ are positive …