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?

  1. PsyDAG

    What do all the dollar signs ($) signify?

  2. Atticus Finch

    They're just a format you can ignore them

  3. AoPS

    Please do not post the questions we give you for homework to other websites.

Respond to this Question

First Name

Your Answer

Similar Questions

  1. 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 …
  2. 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 …
  3. 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 …
  4. 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 $\overline{DE}$, …
  5. 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 $\overline{DE}$, …
  6. 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 …
  7. 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 $AF$?
  8. 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 $\overline{CM}$ …
  9. 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 …
  10. 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 …

More Similar Questions