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#1 2017-03-13 08:14:58

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.


5e95ff0f346c35f3a6cc9ae53d6ce2dc585bb21e.png

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

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

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#2 2017-03-13 20:02:40

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,151

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


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

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#3 2017-03-13 20:49:00

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.


{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.}

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