Math Is Fun Forum

Geomtry.202

Member

Registered: 2017-03-13

Posts: 2

Help on this proof!!

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)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Help on this proof!!

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

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Help on this proof!!

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

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{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.}