Math Is Fun Forum

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Geometry Proof

Can you provide me some hints for 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.
http://latex.artofproblemsolving.com/5/e/9/5e95ff0f346c35f3a6cc9ae53d6ce2dc585bb21e.png

I know I have to use inscribed angles.  Any other helpful hints?
Thanks!

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Geometry Proof

I haven't had time to work on this, but..
is the photo.

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Proof

^

Last edited by thickhead (2016-06-06 16:41:44)

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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.}

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry Proof

This is a popular problem!

Other posts that may help:

- thread opened by Enshrouded_, 23rd Sep 2015
- thread opened by championmathgirl, 9th June 2015
- thread opened by SPARKS_CHAN, 30th Jan 2015

I haven't checked out the solutions, but Bob Bundy posted there and he always gives good advice.

Warning! Be careful with threads on this topic earlier than the three above (there are also two threads from 2014). I got locked out from the forum overnight after clicking multiple times on a 2014 post that opened up a 'forbidden access' page. MIF knows about it now, and unlocked me. If you do get a 'forbidden access' page after clicking on a post, don't click that post again.

Last edited by phrontister (2016-06-08 15:54:38)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Proof

Up till now that has only happened to Agnishom and I.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry Proof

I'm deeply honoured to have joined your club - unintentionally!

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Proof

Think it happened to ganesh also. Certain words are censored by the server.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry Proof

Yes, I knew about censored words, but this one threw me because all I did was click on a search result.

But I clicked it several times, just in case there was some hiccough. If I'd only clicked once (or twice? or thrice?) I may not have been locked out.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Proof

Yes, it was the number of times. The first time you get that error, stop what you are doing.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry Proof

I learnt the hard way. I lost my right arm after the xth click and had to ask MIF to sew it back on again.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Proof

If you know the word that triggered it you are safe in the future.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry Proof

The search word was incircle, which gave 25 results.

I was interested in 6 of them, 4 of which (years 2015 & 2016) opened up fine; but 2 (or was it 1? - I don't recall now) of the older ones (year 2014) opened up the 'forbidden access' page.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Proof

I hope MIF removed whatever word was in those posts.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry Proof

Oh, I see...the word in those posts, not my search word. I sent MIF all the facts that I remembered...

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Proof

That is the first time it has happened to someone accessing a post with some censored word.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,879

Re: Geometry Proof

I'm expert at initiating 'first time' events, like:

- asking a whitegoods service technician why my machine is making an xyz noise: "Sorry, sir, but we've never heard of our machines making an xyz noise before." (maybe I should practise up on making xyz noises over the phone, or send them an mp3 recording of said noise);

- asking Customer Service if there's a fix for this or that: "Oh, we've never been asked about this or that before. Hang on a minute". That's when you discover that your understanding of the length of time a minute takes is way off the mark!

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Proof

#2 Do I need to prove I, the incenter  lies inside

for my proof to hold true?

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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.}

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Re: Geometry Proof

But how do I compute the angles of triangle DEF in terms of the angles of triangle ABC?  I've found 3 isosceles triangles so far, but I don't know what to do with them.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Proof

But why you need to get angles of DEF in terms of ABC? Any way we proved DEF is acute angled triangle.

Last edited by thickhead (2016-06-08 21:02:41)

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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.}