Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**Geomtry.202****Member**- Registered: 2017-03-13
- Posts: 2

Let the incircle of triangle ABC be tangent to sides BC, AC, and AB at D, E, and F, respectively. Prove that triangle DEF is acute. I haven't learned any trig yet. One of the hints were : Compute the angles of triangle DEF in terms of the angles of triangle ABC.

[I added the img tags so that the picture will show -bobbym]

*Last edited by Geomtry.202 (2017-03-13 11:22:21)*

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,322

hi Geomtry.202

Welcome to the forum.

This problem re-appears every few months. Solution here:

http://www.mathisfunforum.com/viewtopic.php?id=20456

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**thickhead****Member**- Registered: 2016-04-16
- Posts: 1,086

Simple. Show that quadrilateral IFBD is cyclic. And use the property of inscribed angle vs.measure of arc.Finished in two lines.

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

Offline

Pages: **1**